diff --git a/src/Bridges/Constraint/bridges/IndicatorToMILPBridge.jl b/src/Bridges/Constraint/bridges/IndicatorToMILPBridge.jl
index 7b31e03d9f..e3e5351881 100644
--- a/src/Bridges/Constraint/bridges/IndicatorToMILPBridge.jl
+++ b/src/Bridges/Constraint/bridges/IndicatorToMILPBridge.jl
@@ -126,9 +126,6 @@ function MOI.delete(
     model::MOI.ModelLike,
     bridge::IndicatorToMILPBridge{T},
 ) where {T}
-    if bridge.slack === nothing
-        return  # final_touch not called, so we can safely skip
-    end
     MOI.delete.(model, bridge.slack_bounds)
     MOI.delete(model, bridge.constraint)
     MOI.delete(model, bridge.slack::MOI.VariableIndex)
diff --git a/src/Bridges/Constraint/bridges/RSOCtoSOCBridge.jl b/src/Bridges/Constraint/bridges/RSOCtoSOCBridge.jl
index c25f678f82..718675d02f 100644
--- a/src/Bridges/Constraint/bridges/RSOCtoSOCBridge.jl
+++ b/src/Bridges/Constraint/bridges/RSOCtoSOCBridge.jl
@@ -59,6 +59,8 @@ end
 
 function MOI.Bridges.map_function(::Type{<:RSOCtoSOCBridge{T}}, func) where {T}
     scalars = MOI.Utilities.eachscalar(func)
+    # We cannot construct MOI.RotatedSecondOrderCone(1)
+    @assert length(scalars) >= 2
     t, u, x = scalars[1], scalars[2], scalars[3:end]
     ts = MOI.Utilities.operate!(/, T, t, sqrt(T(2)))
     us = MOI.Utilities.operate!(/, T, u, sqrt(T(2)))
diff --git a/src/Bridges/Constraint/bridges/SOCtoPSDBridge.jl b/src/Bridges/Constraint/bridges/SOCtoPSDBridge.jl
index 32133a17ff..0d483a9797 100644
--- a/src/Bridges/Constraint/bridges/SOCtoPSDBridge.jl
+++ b/src/Bridges/Constraint/bridges/SOCtoPSDBridge.jl
@@ -256,12 +256,9 @@ end
 
 function MOI.Bridges.map_function(::Type{<:RSOCtoPSDBridge{T}}, func) where {T}
     scalars = MOI.Utilities.eachscalar(func)
-    if length(scalars) < 2
-        error(
-            "Unable to bridge RotatedSecondOrderCone to PSD because the ",
-            "dimension is too small: got $(length(scalars)), expected >= 2.",
-        )
-    elseif length(scalars) == 2
+    # We cannot construct MOI.RotatedSecondOrderCone(1)
+    @assert length(scalars) >= 2
+    if length(scalars) == 2
         return func
     end
     # Input is (t, u, x), and we need [t x'; x 2uI]
diff --git a/src/Bridges/Constraint/bridges/SOCtoRSOCBridge.jl b/src/Bridges/Constraint/bridges/SOCtoRSOCBridge.jl
index af71aa6d88..bc03635030 100644
--- a/src/Bridges/Constraint/bridges/SOCtoRSOCBridge.jl
+++ b/src/Bridges/Constraint/bridges/SOCtoRSOCBridge.jl
@@ -50,13 +50,6 @@ function MOI.Bridges.map_set(
     ::Type{<:SOCtoRSOCBridge},
     set::MOI.SecondOrderCone,
 )
-    if MOI.dimension(set) == 1
-        error(
-            "Unable to reformulate a `SecondOrderCone` into a " *
-            "`RotatedSecondOrderCone` because the dimension of `1` is too " *
-            "small",
-        )
-    end
     return MOI.RotatedSecondOrderCone(MOI.dimension(set))
 end
 
@@ -69,6 +62,14 @@ end
 
 function MOI.Bridges.map_function(::Type{<:SOCtoRSOCBridge{T}}, func) where {T}
     scalars = MOI.Utilities.eachscalar(func)
+    if length(scalars) < 2
+        err = DimensionMismatch(
+            "Unable to reformulate a `SecondOrderCone` into a " *
+            "`RotatedSecondOrderCone` because the output dimension is too " *
+            "small",
+        )
+        throw(err)
+    end
     t, u, x = scalars[1], scalars[2], scalars[3:end]
     ts = MOI.Utilities.operate!(/, T, t, sqrt(T(2)))
     us = MOI.Utilities.operate!(/, T, u, sqrt(T(2)))
diff --git a/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl b/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl
index a704e86755..fb941a73fb 100644
--- a/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl
+++ b/src/Bridges/Constraint/bridges/SOS1ToMILPBridge.jl
@@ -116,9 +116,6 @@ function MOI.get(::MOI.ModelLike, ::MOI.ConstraintSet, bridge::SOS1ToMILPBridge)
 end
 
 function MOI.delete(model::MOI.ModelLike, bridge::SOS1ToMILPBridge)
-    if isempty(bridge.variables)
-        return
-    end
     MOI.delete(model, bridge.equal_to)
     for ci in bridge.less_than
         MOI.delete(model, ci)
diff --git a/src/Bridges/Constraint/bridges/SOS2ToMILPBridge.jl b/src/Bridges/Constraint/bridges/SOS2ToMILPBridge.jl
index 2e25b961fa..e7931d7012 100644
--- a/src/Bridges/Constraint/bridges/SOS2ToMILPBridge.jl
+++ b/src/Bridges/Constraint/bridges/SOS2ToMILPBridge.jl
@@ -116,9 +116,6 @@ function MOI.get(::MOI.ModelLike, ::MOI.ConstraintSet, bridge::SOS2ToMILPBridge)
 end
 
 function MOI.delete(model::MOI.ModelLike, bridge::SOS2ToMILPBridge)
-    if isempty(bridge.variables)
-        return
-    end
     MOI.delete(model, bridge.equal_to)
     for ci in bridge.less_than
         MOI.delete(model, ci)
diff --git a/src/Bridges/Constraint/bridges/ScalarSlackBridge.jl b/src/Bridges/Constraint/bridges/ScalarSlackBridge.jl
index 65ce399a7c..fd7d46ae17 100644
--- a/src/Bridges/Constraint/bridges/ScalarSlackBridge.jl
+++ b/src/Bridges/Constraint/bridges/ScalarSlackBridge.jl
@@ -25,13 +25,6 @@ function MOI.get(
     return 1
 end
 
-function MOI.get(
-    ::_AbstractSlackBridge{T,VF,ZS,F,S},
-    ::MOI.NumberOfConstraints{VF,S},
-)::Int64 where {T,VF,ZS,F,S}
-    return 1
-end
-
 function MOI.get(
     bridge::_AbstractSlackBridge{T,VF,ZS,F},
     ::MOI.ListOfConstraintIndices{F,ZS},
@@ -39,6 +32,13 @@ function MOI.get(
     return [bridge.equality]
 end
 
+function MOI.get(
+    ::_AbstractSlackBridge{T,VF,ZS,F,S},
+    ::MOI.NumberOfConstraints{VF,S},
+)::Int64 where {T,VF,ZS,F,S}
+    return 1
+end
+
 function MOI.get(
     bridge::_AbstractSlackBridge{T,VF,ZS,F,S},
     ::MOI.ListOfConstraintIndices{VF,S},
@@ -55,20 +55,20 @@ function MOI.get(
     # that the original set was the same as the slacked set.
     return error(
         "Internal error: this method should never be called because it " *
-        "represents and invalid state. Please open an issue to report.",
+        "represents an invalid state. Please open an issue to report.",
     )
 end
 
 function MOI.get(
     bridge::_AbstractSlackBridge{T,VF,S,F,S},
-    ::MOI.ListOfConstraintIndices{F,S},
+    ::MOI.ListOfConstraintIndices{VF,S},
 ) where {T,VF,S,F}
     # This method is needed to resolve a possible ambiguity reported by
     # Test.detect_ambiguities. It can't happen in practice because it would mean
     # that the original set was the same as the slacked set.
     return error(
         "Internal error: this method should never be called because it " *
-        "represents and invalid state. Please open an issue to report.",
+        "represents an invalid state. Please open an issue to report.",
     )
 end
 
diff --git a/src/Bridges/Objective/bridge.jl b/src/Bridges/Objective/bridge.jl
index d2b03ddfc4..2bd5fa7042 100644
--- a/src/Bridges/Objective/bridge.jl
+++ b/src/Bridges/Objective/bridge.jl
@@ -95,12 +95,13 @@ end
 
 function MOI.set(
     ::MOI.ModelLike,
-    ::MOI.ObjectiveSense,
+    attr::MOI.ObjectiveSense,
     bridge::AbstractBridge,
     ::MOI.OptimizationSense,
 )
     return throw(
-        ArgumentError(
+        MOI.SetAttributeNotAllowed(
+            attr,
             "Objective bridge of type `$(typeof(bridge))` does not support " *
             "modifying the objective sense. As a workaround, set the sense " *
             "to `MOI.FEASIBILITY_SENSE` to clear the objective function and " *
@@ -111,11 +112,12 @@ end
 
 function MOI.get(
     ::MOI.ModelLike,
-    ::MOI.ObjectiveFunction,
+    attr::MOI.ObjectiveFunction,
     bridge::AbstractBridge,
 )
     return throw(
-        ArgumentError(
+        MOI.GetAttributeNotAllowed(
+            attr,
             "ObjectiveFunction bridge of type `$(typeof(bridge))` does not" *
             " support getting the objective function.",
         ),
diff --git a/src/Bridges/bridge_optimizer.jl b/src/Bridges/bridge_optimizer.jl
index 0a17df458e..f8c335c246 100644
--- a/src/Bridges/bridge_optimizer.jl
+++ b/src/Bridges/bridge_optimizer.jl
@@ -624,6 +624,7 @@ function MOI.delete(b::AbstractBridgeOptimizer, vis::Vector{MOI.VariableIndex})
     else
         MOI.delete(b.model, vis)
     end
+    return
 end
 
 function MOI.delete(b::AbstractBridgeOptimizer, vi::MOI.VariableIndex)
diff --git a/test/Bridges/Constraint/RSOCBridge.jl b/test/Bridges/Constraint/RSOCBridge.jl
index db52767cc0..8bc4bc15c5 100644
--- a/test/Bridges/Constraint/RSOCBridge.jl
+++ b/test/Bridges/Constraint/RSOCBridge.jl
@@ -179,6 +179,26 @@ function test_runtests()
     return
 end
 
+function test_dimension_mismatch_SOCR()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Constraint.SOCR{Float64}(inner)
+    @test_throws(
+        DimensionMismatch,
+        MOI.add_constrained_variables(model, MOI.SecondOrderCone(1)),
+    )
+    return
+end
+
+function test_dimension_mismatch_RSOC()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Constraint.RSOC{Float64}(inner)
+    @test_throws(
+        DimensionMismatch,
+        MOI.add_constrained_variables(model, MOI.RotatedSecondOrderCone(1)),
+    )
+    return
+end
+
 end  # module
 
 TestConstraintRSOC.runtests()
diff --git a/test/Bridges/Constraint/SOCtoPSDBridge.jl b/test/Bridges/Constraint/SOCtoPSDBridge.jl
index 3f91df871b..ae9e1b02fe 100644
--- a/test/Bridges/Constraint/SOCtoPSDBridge.jl
+++ b/test/Bridges/Constraint/SOCtoPSDBridge.jl
@@ -231,6 +231,16 @@ function test_bridging_cost_RSOCtoPSD()
     return
 end
 
+function test_dimension_mismatch_RSOC_to_PSD()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Constraint.RSOCtoPSD{Float64}(inner)
+    @test_throws(
+        DimensionMismatch,
+        MOI.add_constrained_variables(model, MOI.RotatedSecondOrderCone(1)),
+    )
+    return
+end
+
 end  # module
 
 TestConstraintSOCtoPSD.runtests()
diff --git a/test/Bridges/Constraint/ScalarSlackBridge.jl b/test/Bridges/Constraint/ScalarSlackBridge.jl
index 830c0a4a0a..eb5a932fb1 100644
--- a/test/Bridges/Constraint/ScalarSlackBridge.jl
+++ b/test/Bridges/Constraint/ScalarSlackBridge.jl
@@ -411,6 +411,47 @@ function test_runtests()
     return
 end
 
+function test_basis_status()
+    inner = MOI.Utilities.MockOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
+    )
+    model = MOI.Bridges.Constraint.ScalarSlack{Float64}(inner)
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(model, 1.0 * x, MOI.GreaterThan(1.0))
+    y = MOI.get(inner, MOI.ListOfVariableIndices())
+    MOI.set.(inner, MOI.VariableBasisStatus(), y, MOI.BASIC)
+    @test MOI.get(model, MOI.ConstraintBasisStatus(), c) == MOI.BASIC
+    d = MOI.add_constraint(model, 1.0 * x, MOI.Interval(1.0, 2.0))
+    z = last(MOI.get(inner, MOI.ListOfVariableIndices()))
+    MOI.set(inner, MOI.VariableBasisStatus(), z, MOI.SUPER_BASIC)
+    @test MOI.get(model, MOI.ConstraintBasisStatus(), d) == MOI.SUPER_BASIC
+    return
+end
+
+function test_internal_error()
+    F, S = MOI.ScalarAffineFunction{Float64}, MOI.EqualTo{Float64}
+    BT = MOI.Bridges.Constraint.ScalarSlackBridge{Float64,F,S}
+    model = MOI.Utilities.Model{Float64}()
+    x = MOI.add_variable(model)
+    set = MOI.EqualTo(1.0)
+    bridge = MOI.Bridges.Constraint.bridge_constraint(BT, model, 1.0 * x, set)
+    @test_throws(
+        ErrorException(
+            "Internal error: this method should never be called because it " *
+            "represents an invalid state. Please open an issue to report.",
+        ),
+        MOI.get(bridge, MOI.NumberOfConstraints{MOI.VariableIndex,S}()),
+    )
+    @test_throws(
+        ErrorException(
+            "Internal error: this method should never be called because it " *
+            "represents an invalid state. Please open an issue to report.",
+        ),
+        MOI.get(bridge, MOI.ListOfConstraintIndices{MOI.VariableIndex,S}()),
+    )
+    return
+end
+
 end  # module
 
 TestConstraintSlack.runtests()
diff --git a/test/Bridges/Constraint/SplitIntervalBridge.jl b/test/Bridges/Constraint/SplitIntervalBridge.jl
index 79009370e5..21395cad26 100644
--- a/test/Bridges/Constraint/SplitIntervalBridge.jl
+++ b/test/Bridges/Constraint/SplitIntervalBridge.jl
@@ -499,6 +499,33 @@ function test_runtests_vector()
     return
 end
 
+function test_get_function()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Constraint.SplitInterval{Float64}(inner)
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(model, 1.0 * x, MOI.Interval(-Inf, Inf))
+    @test MOI.get(model, MOI.ConstraintFunction(), c) ≈ 1.0 * x
+    return
+end
+
+function test_modify_set()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Constraint.SplitInterval{Float64}(inner)
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(model, 1.0 * x, MOI.Interval(-Inf, Inf))
+    for set in [
+        MOI.Interval(-Inf, Inf),
+        MOI.Interval(1.0, 2.0),
+        MOI.Interval(2.0, 3.0),
+        MOI.Interval(-Inf, Inf),
+    ]
+        MOI.set(model, MOI.ConstraintSet(), c, set)
+        @test MOI.get(model, MOI.ConstraintSet(), c) == set
+        @test MOI.get(model, MOI.ConstraintFunction(), c) ≈ 1.0 * x
+    end
+    return
+end
+
 end  # module
 
 TestConstraintSplitInterval.runtests()
diff --git a/test/Bridges/Constraint/VectorizeBridge.jl b/test/Bridges/Constraint/VectorizeBridge.jl
index fefbe0fc4a..e17e9c4e42 100644
--- a/test/Bridges/Constraint/VectorizeBridge.jl
+++ b/test/Bridges/Constraint/VectorizeBridge.jl
@@ -285,6 +285,22 @@ function test_VectorNonlinearFunction()
     return
 end
 
+function test_constraint_primal_ray()
+    inner = MOI.Utilities.MockOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
+    )
+    model = MOI.Bridges.Constraint.Vectorize{Float64}(inner)
+    x = MOI.add_variable(model)
+    c = MOI.add_constraint(model, 1.0 * x, MOI.EqualTo(3.0))
+    MOI.set(inner, MOI.PrimalStatus(), MOI.INFEASIBILITY_CERTIFICATE)
+    y = only(MOI.get(inner, MOI.ListOfVariableIndices()))
+    MOI.set(inner, MOI.VariablePrimal(), y, 1.23)
+    @test MOI.get(model, MOI.ConstraintPrimal(), c) == 1.23
+    MOI.set(inner, MOI.PrimalStatus(), MOI.FEASIBLE_POINT)
+    @test MOI.get(model, MOI.ConstraintPrimal(), c) == 1.23
+    return
+end
+
 end  # module
 
 TestConstraintVectorize.runtests()
diff --git a/test/Bridges/Objective/SlackBridge.jl b/test/Bridges/Objective/SlackBridge.jl
index 68fb70e2e7..9757aae392 100644
--- a/test/Bridges/Objective/SlackBridge.jl
+++ b/test/Bridges/Objective/SlackBridge.jl
@@ -46,7 +46,7 @@ function test_SlackBridge_ObjectiveSense_modify()
     MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
     @test_throws(
-        ArgumentError,
+        MOI.SetAttributeNotAllowed,
         MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE),
     )
     MOI.set(model, MOI.ObjectiveSense(), MOI.FEASIBILITY_SENSE)
@@ -328,7 +328,8 @@ function test_original()
             ("y", MOI.GreaterThan{Float64}(2.0)),
         ],
     )
-    err = ArgumentError(
+    err = MOI.SetAttributeNotAllowed(
+        MOI.ObjectiveSense(),
         "Objective bridge of type `$(MOI.Bridges.Objective.SlackBridge{Float64,MOI.ScalarQuadraticFunction{Float64},MOI.ScalarQuadraticFunction{Float64}})`" *
         " does not support modifying the objective sense. As a workaround, set" *
         " the sense to `MOI.FEASIBILITY_SENSE` to clear the objective function" *
diff --git a/test/Bridges/Variable/HermitianToSymmetricPSDBridge.jl b/test/Bridges/Variable/HermitianToSymmetricPSDBridge.jl
index 151dca914e..d018e74589 100644
--- a/test/Bridges/Variable/HermitianToSymmetricPSDBridge.jl
+++ b/test/Bridges/Variable/HermitianToSymmetricPSDBridge.jl
@@ -113,6 +113,28 @@ function test_runtests()
     return
 end
 
+function test_delete()
+    inner = MOI.Utilities.Model{Float64}()
+    model = MOI.Bridges.Variable.HermitianToSymmetricPSD{Float64}(inner)
+    set = MOI.HermitianPositiveSemidefiniteConeTriangle(2)
+    x, _ = MOI.add_constrained_variables(model, set)
+    MOI.delete(model, x)
+    @test MOI.is_empty(inner)
+    return
+end
+
+function test_set_variable_primal_start()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Variable.HermitianToSymmetricPSD{Float64}(inner)
+    set = MOI.HermitianPositiveSemidefiniteConeTriangle(2)
+    x, _ = MOI.add_constrained_variables(model, set)
+    MOI.set(model, MOI.VariablePrimalStart(), x[1], 1.0)
+    @test MOI.get(model, MOI.VariablePrimalStart(), x[1]) == 1.0
+    MOI.set(model, MOI.VariablePrimalStart(), x[1], nothing)
+    @test MOI.get(model, MOI.VariablePrimalStart(), x[1]) === nothing
+    return
+end
+
 end  # module
 
 TestVariableHermitianToSymmetricPSD.runtests()
diff --git a/test/Bridges/Variable/NonposToNonnegBridge.jl b/test/Bridges/Variable/NonposToNonnegBridge.jl
index 93381d1b25..6d7f00a213 100644
--- a/test/Bridges/Variable/NonposToNonnegBridge.jl
+++ b/test/Bridges/Variable/NonposToNonnegBridge.jl
@@ -199,6 +199,14 @@ function test_runtests()
     return
 end
 
+function test_adjoint_map_function()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Variable.NonposToNonneg{Float64}(inner)
+    x, _ = MOI.add_constrained_variables(model, MOI.Nonpositives(1))
+    @test MOI.Bridges.adjoint_map_function(model.map[only(x)], 1.23) == -1.23
+    return
+end
+
 end  # module
 
 TestVariableFlipSign.runtests()
diff --git a/test/Bridges/Variable/RSOCtoSOCBridge.jl b/test/Bridges/Variable/RSOCtoSOCBridge.jl
index 0134868226..695e9c28a4 100644
--- a/test/Bridges/Variable/RSOCtoSOCBridge.jl
+++ b/test/Bridges/Variable/RSOCtoSOCBridge.jl
@@ -144,6 +144,15 @@ function test_runtests()
     return
 end
 
+function test_adjoint_map_function()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Variable.RSOCtoSOC{Float64}(inner)
+    x, _ = MOI.add_constrained_variables(model, MOI.RotatedSecondOrderCone(3))
+    @test MOI.Bridges.adjoint_map_function(model.map[first(x)], [2, 0.5, 1]) ≈
+          [2.5 / sqrt(2), +1.5 / sqrt(2), 1.0]
+    return
+end
+
 end  # module
 
 TestVariableRSOCtoSOC.runtests()
diff --git a/test/Bridges/Variable/SOCtoRSOCBridge.jl b/test/Bridges/Variable/SOCtoRSOCBridge.jl
index cd65caf75d..59388e51aa 100644
--- a/test/Bridges/Variable/SOCtoRSOCBridge.jl
+++ b/test/Bridges/Variable/SOCtoRSOCBridge.jl
@@ -151,6 +151,15 @@ function test_runtests()
     return
 end
 
+function test_adjoint_map_function()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Variable.SOCtoRSOC{Float64}(inner)
+    x, _ = MOI.add_constrained_variables(model, MOI.SecondOrderCone(3))
+    @test MOI.Bridges.adjoint_map_function(model.map[first(x)], [2, 0.5, 1]) ≈
+          [2.5 / sqrt(2), +1.5 / sqrt(2), 1.0]
+    return
+end
+
 end  # module
 
 TestVariableSOCtoRSOC.runtests()
diff --git a/test/Bridges/Variable/VectorizeBridge.jl b/test/Bridges/Variable/VectorizeBridge.jl
index 4148623501..0f732cbc8e 100644
--- a/test/Bridges/Variable/VectorizeBridge.jl
+++ b/test/Bridges/Variable/VectorizeBridge.jl
@@ -287,6 +287,30 @@ function test_runtests()
     return
 end
 
+function test_list_of_constraint_indices()
+    inner = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    model = MOI.Bridges.Variable.Vectorize{Float64}(inner)
+    x, _ = MOI.add_constrained_variable(model, MOI.EqualTo(1.0))
+    attr = MOI.ListOfConstraintIndices{MOI.VectorOfVariables,MOI.Zeros}()
+    @test isempty(MOI.get(model, attr))
+    return
+end
+
+function test_variable_primal_ray()
+    inner = MOI.Utilities.MockOptimizer(
+        MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),
+    )
+    model = MOI.Bridges.Variable.Vectorize{Float64}(inner)
+    x, _ = MOI.add_constrained_variable(model, MOI.EqualTo(1.0))
+    MOI.set(inner, MOI.PrimalStatus(), MOI.INFEASIBILITY_CERTIFICATE)
+    y = only(MOI.get(inner, MOI.ListOfVariableIndices()))
+    MOI.set(inner, MOI.VariablePrimal(), y, 1.23)
+    @test MOI.get(model, MOI.VariablePrimal(), x) == 1.23
+    MOI.set(inner, MOI.PrimalStatus(), MOI.FEASIBLE_POINT)
+    @test MOI.get(model, MOI.VariablePrimal(), x) == 2.23
+    return
+end
+
 end  # module
 
 TestVariableVectorize.runtests()
diff --git a/test/Bridges/Variable/bridge.jl b/test/Bridges/Variable/bridge.jl
index 86961fdc3e..85389328f6 100644
--- a/test/Bridges/Variable/bridge.jl
+++ b/test/Bridges/Variable/bridge.jl
@@ -49,6 +49,15 @@ function test_AbstractBridge()
     return
 end
 
+function test_bridging_cost()
+    model = MOI.Bridges.Variable.SingleBridgeOptimizer{DummyVariableBridge}(
+        MOI.Utilities.Model{Float64}(),
+    )
+    @test MOI.Bridges.bridging_cost(model) == 1.0
+    @test MOI.Bridges.bridging_cost(model, MOI.ZeroOne) == 1.0
+    return
+end
+
 end  # module
 
 TestVariableBridge.runtests()
diff --git a/test/Bridges/bridge_optimizer.jl b/test/Bridges/bridge_optimizer.jl
index 879a54a4c9..faf7af6b9c 100644
--- a/test/Bridges/bridge_optimizer.jl
+++ b/test/Bridges/bridge_optimizer.jl
@@ -1286,6 +1286,134 @@ function test_issue_2452_integer()
     return
 end
 
+struct EmptyBridgeOptimizer <: MOI.Bridges.AbstractBridgeOptimizer end
+
+function test_supports_bridging_constrained_variable_fallback()
+    @test !MOI.Bridges.supports_bridging_constrained_variable(
+        EmptyBridgeOptimizer(),
+        MOI.ZeroOne,
+    )
+    return
+end
+
+function test_supports_bridging_constraint_fallback()
+    @test !MOI.Bridges.supports_bridging_constraint(
+        EmptyBridgeOptimizer(),
+        MOI.ScalarAffineFunction{Float64},
+        MOI.EqualTo{Float64},
+    )
+    return
+end
+
+function test_delete_variable_from_bridged_objective()
+    model = MOI.Utilities.Model{Float64}()
+    b = MOI.Bridges.Objective.VectorFunctionize{Float64}(model)
+    x = MOI.add_variables(b, 2)
+    y = MOI.add_variable(b)
+    f = MOI.VectorOfVariables(x)
+    MOI.set(b, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    MOI.set(b, MOI.ObjectiveFunction{typeof(f)}(), f)
+    G = MOI.VectorAffineFunction{Float64}
+    g = MOI.get(model, MOI.ObjectiveFunction{G}())
+    MOI.delete(b, y)
+    @test g ≈ MOI.get(model, MOI.ObjectiveFunction{G}())
+    MOI.delete(b, x[1])
+    @test ≈(
+        MOI.Utilities.vectorize([MOI.Utilities.scalarize(g)[2]]),
+        MOI.get(model, MOI.ObjectiveFunction{G}()),
+    )
+    MOI.delete(b, x[2])
+    @test ≈(
+        MOI.Utilities.vectorize([zero(MOI.ScalarAffineFunction{Float64})]),
+        MOI.get(model, MOI.ObjectiveFunction{G}()),
+    )
+    return
+end
+
+function test_get_ObjectiveFunctionValue()
+    model = MOI.Utilities.MockOptimizer(MOI.Utilities.Model{Float64}())
+    b = MOI.Bridges.full_bridge_optimizer(model, Float64)
+    x = MOI.add_variable(b)
+    MOI.set(b, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    MOI.set(b, MOI.ObjectiveFunction{MOI.VariableIndex}(), x)
+    y = only(MOI.get(model, MOI.ListOfVariableIndices()))
+    MOI.set(model, MOI.VariablePrimal(1), y, 1.23)
+    @test MOI.get(b, MOI.Bridges.ObjectiveFunctionValue{typeof(x)}(1)) == 1.23
+    return
+end
+
+function test_bridged_function()
+    model = MOI.Utilities.Model{Float64}()
+    b = MOI.Bridges.Variable.Free{Float64}(model)
+    x = MOI.add_variable(b)
+    y, _ = MOI.add_constrained_variable(b, MOI.GreaterThan(1.0))
+    @test_throws(
+        ErrorException("Using bridged variable in `VariableIndex` function."),
+        MOI.Bridges.bridged_function(b, x),
+    )
+    @test MOI.Bridges.bridged_function(b, y) == y
+    return
+end
+
+function test_bridged_constraint_function_no_variable_bridges()
+    model = MOI.Utilities.Model{Float64}()
+    bridged = MOI.Bridges.full_bridge_optimizer(model, Float64)
+    x = MOI.add_variable(bridged)
+    set = MOI.ZeroOne()
+    @test MOI.Bridges.bridged_constraint_function(bridged, x, set) == (x, set)
+    return
+end
+
+function test_bridged_constraint_function_with_variable_bridges()
+    model = MOI.Utilities.Model{Float64}()
+    b = MOI.Bridges.Variable.Free{Float64}(model)
+    x = MOI.add_variable(b)
+    set = MOI.ZeroOne()
+    f, set = MOI.Bridges.bridged_constraint_function(b, 1.0 * x, set)
+    @test set == MOI.ZeroOne()
+    y = MOI.get(model, MOI.ListOfVariableIndices())
+    @test f ≈ 1.0 * y[1] - 1.0 * y[2]
+    return
+end
+
+struct EmptyObjectiveBridge <: MOI.Bridges.Objective.AbstractBridge end
+
+function test_fallback_bridge_objective()
+    model = MOI.Utilities.Model{Float64}()
+    x = MOI.add_variable(model)
+    @test_throws(
+        MOI.UnsupportedAttribute(MOI.ObjectiveFunction{MOI.VariableIndex}()),
+        MOI.Bridges.Objective.bridge_objective(EmptyObjectiveBridge, model, x),
+    )
+    return
+end
+
+function test_fallback_set_objective_sense()
+    model = MOI.Utilities.Model{Float64}()
+    bridge = EmptyObjectiveBridge()
+    @test_throws(
+        MOI.SetAttributeNotAllowed{MOI.ObjectiveSense},
+        MOI.set(model, MOI.ObjectiveSense(), bridge, MOI.MIN_SENSE),
+    )
+    return
+end
+
+function test_fallback_get_objective_function()
+    model = MOI.Utilities.Model{Float64}()
+    attr = MOI.ObjectiveFunction{MOI.VariableIndex}()
+    @test_throws(
+        MOI.GetAttributeNotAllowed{typeof(attr)},
+        MOI.get(model, attr, EmptyObjectiveBridge()),
+    )
+    return
+end
+
+function test_fallback_delete_objective_bridge()
+    model = MOI.Utilities.Model{Float64}()
+    @test_throws ArgumentError MOI.delete(model, EmptyObjectiveBridge())
+    return
+end
+
 end  # module
 
 TestBridgeOptimizer.runtests()
diff --git a/test/Bridges/debug.jl b/test/Bridges/debug.jl
index 386116be21..700c828ca2 100644
--- a/test/Bridges/debug.jl
+++ b/test/Bridges/debug.jl
@@ -314,6 +314,23 @@ function test_print_active_bridges_variable_bridged_with_constraint()
     return
 end
 
+function test_print_graph_stdout()
+    model = MOI.Utilities.Model{Float64}()
+    bridged = MOI.Bridges.full_bridge_optimizer(model, Float64)
+    dir = mktempdir()
+    filename = joinpath(dir, "tmp.out")
+    open(filename, "w") do io
+        redirect_stdout(io) do
+            MOI.Bridges.print_graph(bridged)
+            return
+        end
+        return
+    end
+    @test read(filename, String) ==
+          "Bridge graph with 0 variable nodes, 0 constraint nodes and 0 objective nodes.\n"
+    return
+end
+
 end
 
 TestBridgesDebug.runtests()