diff --git a/src/adjtrans.jl b/src/adjtrans.jl
index 40a26f1c..f889d37c 100644
--- a/src/adjtrans.jl
+++ b/src/adjtrans.jl
@@ -552,3 +552,20 @@ conj(A::Adjoint) = transpose(A.parent)
 function Base.replace_in_print_matrix(A::AdjOrTrans,i::Integer,j::Integer,s::AbstractString)
     Base.replace_in_print_matrix(parent(A), j, i, s)
 end
+
+# Special adjoint/transpose methods for Adjoint/Transpose that have been reshaped as a vector
+# these are used in transposing banded matrices by forwarding the operation to the bands
+"""
+    _vectranspose(A::AbstractVector)::AbstractVector
+
+Compute `vec(transpose(A))`, but avoid an allocating reshape if possible
+"""
+_vectranspose(A::AbstractVector) = vec(transpose(A))
+_vectranspose(A::Base.ReshapedArray{<:Any,1,<:TransposeAbsVec}) = transpose(parent(A))
+"""
+    _vecadjoint(A::AbstractVector)::AbstractVector
+
+Compute `vec(adjoint(A))`, but avoid an allocating reshape if possible
+"""
+_vecadjoint(A::AbstractVector) = vec(adjoint(A))
+_vecadjoint(A::Base.ReshapedArray{<:Any,1,<:AdjointAbsVec}) = adjoint(parent(A))
diff --git a/src/bidiag.jl b/src/bidiag.jl
index a37f4094..6c61e9fa 100644
--- a/src/bidiag.jl
+++ b/src/bidiag.jl
@@ -308,12 +308,8 @@ for func in (:conj, :copy, :real, :imag)
 end
 isreal(M::Bidiagonal) = isreal(M.dv) && isreal(M.ev)
 
-adjoint(B::Bidiagonal{<:Number}) = Bidiagonal(vec(adjoint(B.dv)), vec(adjoint(B.ev)), B.uplo == 'U' ? :L : :U)
-adjoint(B::Bidiagonal{<:Number, <:Base.ReshapedArray{<:Number,1,<:Adjoint}}) =
-    Bidiagonal(adjoint(parent(B.dv)), adjoint(parent(B.ev)), B.uplo == 'U' ? :L : :U)
-adjoint(B::Bidiagonal) = Bidiagonal(adjoint.(B.dv), adjoint.(B.ev), B.uplo == 'U' ? :L : :U)
-transpose(B::Bidiagonal{<:Number}) = Bidiagonal(B.dv, B.ev, B.uplo == 'U' ? :L : :U)
-transpose(B::Bidiagonal) = Bidiagonal(transpose.(B.dv), transpose.(B.ev), B.uplo == 'U' ? :L : :U)
+adjoint(B::Bidiagonal) = Bidiagonal(_vecadjoint(B.dv), _vecadjoint(B.ev), B.uplo == 'U' ? :L : :U)
+transpose(B::Bidiagonal) = Bidiagonal(_vectranspose(B.dv), _vectranspose(B.ev), B.uplo == 'U' ? :L : :U)
 permutedims(B::Bidiagonal) = Bidiagonal(B.dv, B.ev, B.uplo == 'U' ? 'L' : 'U')
 function permutedims(B::Bidiagonal, perm)
     Base.checkdims_perm(axes(B), axes(B), perm)
diff --git a/src/diagonal.jl b/src/diagonal.jl
index 2b1df153..f95d5979 100644
--- a/src/diagonal.jl
+++ b/src/diagonal.jl
@@ -906,11 +906,8 @@ end
 end
 
 conj(D::Diagonal) = Diagonal(conj(D.diag))
-transpose(D::Diagonal{<:Number}) = D
-transpose(D::Diagonal) = Diagonal(transpose.(D.diag))
-adjoint(D::Diagonal{<:Number}) = Diagonal(vec(adjoint(D.diag)))
-adjoint(D::Diagonal{<:Number,<:Base.ReshapedArray{<:Number,1,<:Adjoint}}) = Diagonal(adjoint(parent(D.diag)))
-adjoint(D::Diagonal) = Diagonal(adjoint.(D.diag))
+transpose(D::Diagonal) = Diagonal(_vectranspose(D.diag))
+adjoint(D::Diagonal) = Diagonal(_vecadjoint(D.diag))
 permutedims(D::Diagonal) = D
 permutedims(D::Diagonal, perm) = (Base.checkdims_perm(axes(D), axes(D), perm); D)
 
diff --git a/test/bidiag.jl b/test/bidiag.jl
index 01577d4e..bccaedf5 100644
--- a/test/bidiag.jl
+++ b/test/bidiag.jl
@@ -1240,4 +1240,19 @@ end
     @test_throws BoundsError B[LinearAlgebra.BandIndex(0,size(B,1)+1)]
 end
 
+@testset "lazy adjtrans" begin
+    B = Bidiagonal(fill([1 2; 3 4], 3), fill([5 6; 7 8], 2), :U)
+    m = [2 4; 6 8]
+    for op in (transpose, adjoint)
+        C = op(B)
+        el = op(m)
+        C[1,1] = el
+        @test B[1,1] == m
+        C[2,1] = el
+        @test B[1,2] == m
+        @test (@allocated op(B)) == 0
+        @test (@allocated op(op(B))) == 0
+    end
+end
+
 end # module TestBidiagonal
diff --git a/test/diagonal.jl b/test/diagonal.jl
index e3724162..1c85153f 100644
--- a/test/diagonal.jl
+++ b/test/diagonal.jl
@@ -1515,4 +1515,17 @@ end
     @test_throws BoundsError D[LinearAlgebra.BandIndex(0,size(D,1)+1)]
 end
 
+@testset "lazy adjtrans" begin
+    D = Diagonal(fill([1 2; 3 4], 3))
+    m = [2 4; 6 8]
+    for op in (transpose, adjoint)
+        C = op(D)
+        el = op(m)
+        C[1,1] = el
+        @test D[1,1] == m
+        @test (@allocated op(D)) == 0
+        @test (@allocated op(op(D))) == 0
+    end
+end
+
 end # module TestDiagonal