diff --git a/src/adjtrans.jl b/src/adjtrans.jl
index f7caa9bc..d81aa3ae 100644
--- a/src/adjtrans.jl
+++ b/src/adjtrans.jl
@@ -319,8 +319,8 @@ const AdjointAbsVec{T} = Adjoint{T,<:AbstractVector}
 const AdjointAbsMat{T} = Adjoint{T,<:AbstractMatrix}
 const TransposeAbsVec{T} = Transpose{T,<:AbstractVector}
 const TransposeAbsMat{T} = Transpose{T,<:AbstractMatrix}
-const AdjOrTransAbsVec{T} = AdjOrTrans{T,<:AbstractVector}
-const AdjOrTransAbsMat{T} = AdjOrTrans{T,<:AbstractMatrix}
+const AdjOrTransAbsVec{T,V<:AbstractVector} = AdjOrTrans{T,V}
+const AdjOrTransAbsMat{T,M<:AbstractMatrix} = AdjOrTrans{T,M}
 
 # for internal use below
 wrapperop(_) = identity
diff --git a/src/diagonal.jl b/src/diagonal.jl
index 27ff3b1f..5618c313 100644
--- a/src/diagonal.jl
+++ b/src/diagonal.jl
@@ -330,6 +330,28 @@ function (*)(D::Diagonal, V::AbstractVector)
     return D.diag .* V
 end
 
+function _diag_adj_mul(A::AdjOrTransAbsMat, D::Diagonal)
+    adj = wrapperop(A)
+    copy(adj(adj(D) * adj(A)))
+end
+function _diag_adj_mul(A::AdjOrTransAbsMat{<:Number, <:StridedMatrix}, D::Diagonal{<:Number})
+    @invoke *(A::AbstractMatrix, D::AbstractMatrix)
+end
+function _diag_adj_mul(D::Diagonal, A::AdjOrTransAbsMat)
+    adj = wrapperop(A)
+    copy(adj(adj(A) * adj(D)))
+end
+function _diag_adj_mul(D::Diagonal{<:Number}, A::AdjOrTransAbsMat{<:Number, <:StridedMatrix})
+    @invoke *(D::AbstractMatrix, A::AbstractMatrix)
+end
+
+function (*)(A::AdjOrTransAbsMat, D::Diagonal)
+    _diag_adj_mul(A, D)
+end
+function (*)(D::Diagonal, A::AdjOrTransAbsMat)
+    _diag_adj_mul(D, A)
+end
+
 function rmul!(A::AbstractMatrix, D::Diagonal)
     matmul_size_check(size(A), size(D))
     for I in CartesianIndices(A)