diff --git a/src/hagerzhang.jl b/src/hagerzhang.jl
index 9d1be56..61a0b4d 100644
--- a/src/hagerzhang.jl
+++ b/src/hagerzhang.jl
@@ -92,6 +92,7 @@ Conjugate gradient line search implementation from:
    display::Int = 0
    mayterminate::Tm = Ref{Bool}(false)
    cache::Union{Nothing,LineSearchCache{T}} = nothing
+   check_flatness::Bool = false
 end
 HagerZhang{T}(args...; kwargs...) where T = HagerZhang{T, Base.RefValue{Bool}}(args...; kwargs...)
 
@@ -285,12 +286,13 @@ function (ls::HagerZhang)(ϕ, ϕdϕ,
             if display & LINESEARCH > 0
                 println("Linesearch: secant succeeded")
             end
-            if nextfloat(values[ia]) >= values[ib] && nextfloat(values[iA]) >= values[iB]
+            if ls.check_flatness && nextfloat(values[ia]) >= values[ib] && nextfloat(values[iA]) >= values[iB]
                 # It's so flat, secant didn't do anything useful, time to quit
                 if display & LINESEARCH > 0
                     println("Linesearch: secant suggests it's flat")
                 end
                 mayterminate[] = false # reset in case another initial guess is used next
+
                 return A, values[iA]
             end
             ia = iA
diff --git a/test/captured.jl b/test/captured.jl
index 05b81fa..d6d97f7 100644
--- a/test/captured.jl
+++ b/test/captured.jl
@@ -31,5 +31,5 @@ end
     fdf = OnceDifferentiable(tc)
     hz = HagerZhang()
     α, val = hz(fdf.f, fdf.fdf, 1.0, fdf.fdf(0.0)...)
-    @test_broken val <= minimum(tc)
+    @test val <= minimum(tc)
 end
diff --git a/test/issues.jl b/test/issues.jl
index d0d01f4..687907e 100644
--- a/test/issues.jl
+++ b/test/issues.jl
@@ -3,32 +3,32 @@ using LineSearches, LinearAlgebra, Test
 
 A = randn(100, 100)
 x0 = randn(100)
-b = A*x0
+b = A * x0
 
 # Objective function and gradient
-f(x) = .5*norm(A*x - b)^2
-g!(gvec, x) = (gvec .= A'*(A*x-b))
+f(x) = 0.5 * norm(A * x - b)^2
+g!(gvec, x) = (gvec .= A' * (A * x - b))
 fg!(gvec, x) = (g!(gvec, x); return f(x))
 
 # Init
-x = 1f1*randn(100)
+x = 1.0f1 * randn(100)
 gv = similar(x)
 
 # Line search
-α0 = 1f-3
+α0 = 1.0f-3
 ϕ0 = fg!(gv, x)
-s = -1*gv
+s = -1 * gv
 dϕ0 = dot(gv, s)
 println(ϕ0, ", ", dϕ0)
 
 # Univariate line search functions
-ϕ(α) = f(x .+ α.*s)
+ϕ(α) = f(x .+ α .* s)
 function dϕ(α)
-    g!(gv, x .+ α.*s)
+    g!(gv, x .+ α .* s)
     return dot(gv, s)
 end
 function ϕdϕ(α)
-    phi = fg!(gv, x .+ α.*s)
+    phi = fg!(gv, x .+ α .* s)
     dphi = dot(gv, s)
     return (phi, dphi)
 end
@@ -36,3 +36,140 @@ end
 res = (StrongWolfe())(ϕ, dϕ, ϕdϕ, α0, ϕ0, dϕ0)
 @test res[2] > 0
 @test res[2] == ϕ(res[1])
+
+@testset "HZ convergence issues" begin
+    @testset "Flatness check issues" begin
+        function prepare_test_case(; alphas, values, slopes)
+            perm = sortperm(alphas)
+            alphas = alphas[perm]
+            push!(alphas, alphas[end] + 1)
+            values = values[perm]
+            push!(values, values[end])
+            slopes = slopes[perm]
+            push!(slopes, 0.0)
+            return LineSearchTestCase(alphas, values, slopes)
+        end
+
+        tc1 = prepare_test_case(;
+            alphas = [0.0, 1.0, 5.0, 3.541670844449739],
+            values = [
+                3003.592409634743,
+                2962.0378569864743,
+                2891.4462095232184,
+                3000.9760725116876,
+            ],
+            slopes = [
+                -22332.321416890798,
+                -20423.214551925797,
+                11718.185026267562,
+                -22286.821227217057,
+            ],
+        )
+
+        function tc_to_f(tc)
+            function f(x)
+                i = findfirst(u -> u > x, tc.alphas) - 1
+                xk = tc.alphas[i]
+                xkp1 = tc.alphas[i+1]
+                dx = xkp1 - xk
+                t = (x - xk) / dx
+                h00t = 2t^3 - 3t^2 + 1
+                h10t = t * (1 - t)^2
+                h01t = t^2 * (3 - 2t)
+                h11t = t^2 * (t - 1)
+                val =
+                    h00t * tc.values[i] +
+                    h10t * dx * tc.slopes[i] +
+                    h01t * tc.values[i+1] +
+                    h11t * dx * tc.slopes[i+1]
+
+                return val
+            end
+        end
+        function tc_to_fdf(tc)
+            function fdf(x)
+                i = findfirst(u -> u > x, tc.alphas) - 1
+                xk = tc.alphas[i]
+                xkp1 = tc.alphas[i+1]
+                dx = xkp1 - xk
+                t = (x - xk) / dx
+                h00t = 2t^3 - 3t^2 + 1
+                h10t = t * (1 - t)^2
+                h01t = t^2 * (3 - 2t)
+                h11t = t^2 * (t - 1)
+                val =
+                    h00t * tc.values[i] +
+                    h10t * dx * tc.slopes[i] +
+                    h01t * tc.values[i+1] +
+                    h11t * dx * tc.slopes[i+1]
+
+                h00tp = 6t^2 - 6t
+                h10tp = 3t^2 - 4t + 1
+                h01tp = -6t^2 + 6 * t
+                h11tp = 3t^2 - 2t
+                slope =
+                    (
+                        h00tp * tc.values[i] +
+                        h10tp * dx * tc.slopes[i] +
+                        h01tp * tc.values[i+1] +
+                        h11tp * dx * tc.slopes[i+1]
+                    ) / dx
+                println(x, " ", val, " ", slope)
+                return val, slope
+            end
+        end
+
+        function test_tc(tc, check_flatness)
+            cache = LineSearchCache{Float64}()
+            hz = HagerZhang(; cache, check_flatness)
+            f = tc_to_f(tc)
+            fdf = tc_to_fdf(tc)
+            hz(f, fdf, 1.0, fdf(0.0)...), cache
+        end
+
+        res, res_cache = test_tc(tc1, true)
+        @show res
+        @show res_cache
+        @test_broken minimum(res_cache.values) == res[2]
+
+        res2, res_cache2 = test_tc(tc1, false)
+        @test minimum(res_cache2.values) == res2[2]
+        #=
+        using AlgebraOfGraphics, CairoMakie
+        draw(data((x=0.0:0.05:5.5, y=map(x->tc_to_f(tc1)(x), 0:0.05:5.5)))*mapping(:x,:y)*visual(Scatter)+
+        data((alphas=res_cache.alphas, values=res_cache.values))*mapping(:alphas,:values)*visual(Scatter; color=:red))
+        =#
+    end
+
+    # should add as upstream
+    #=
+    @testset "from kbarros" begin
+        # The minimizer is x0=[0, 2πn/100], with f(x0) = 1. Any integer n is fine.
+        function f(x)
+            return (x[1]^2 + 1) * (2 - cos(100*x[2]))
+        end
+
+        using Optim
+
+        function test_converges(method)
+            for i in 1:100
+                r = randn(2)
+                res = optimize(f, r, method)
+                if Optim.converged(res) && minimum(res) > f([0,0]) + 1e-8
+                    println("""
+                        Incorrectly reported convergence after $(res.iterations) iterations
+                        Reached x = $(Optim.minimizer(res)) with f(x) = $(minimum(res))
+                        """)
+                end
+            end
+        end
+
+        # Works successfully, no printed output
+        test_converges(LBFGS(; linesearch=Optim.LineSearches.BackTracking(order=2)))
+
+        # Prints ~10 failures to converge (in 100 tries). Frequently fails after the
+        # first line search.
+        test_converges(ConjugateGradient(; linesearch=Optim.LineSearches.HagerZhang(check_flatness=false)))
+    end
+    =#
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 4910d53..011bc22 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -15,7 +15,8 @@ my_tests = [
     "alphacalc.jl",
     "arbitrary_precision.jl",
     "examples.jl",
-    "captured.jl"
+    "captured.jl",
+    "issues.jl",
 ]
 
 mutable struct StateDummy