diff --git a/src/base.jl b/src/base.jl
index 2fd26b4..5adb77f 100644
--- a/src/base.jl
+++ b/src/base.jl
@@ -31,6 +31,7 @@ using LinearAlgebra
 const wrappers = (
   :(SubArray{<:Any,<:Any,AT})                     => (A,mut)->SubArray(mut(parent(A)), mut(parentindices(A))),
   :(PermutedDimsArray{<:Any,<:Any,<:Any,<:Any,AT})=> (A,mut)->PermutedDimsArray(mut(parent(A)), permutation(A)),
+  :(Base.ReshapedArray{<:Any,<:Any,AT,<:Any})     => (A,mut)->Base.reshape(mut(parent(A)), size(A)),
   :(LinearAlgebra.Adjoint{<:Any,AT})              => (A,mut)->LinearAlgebra.adjoint(mut(parent(A))),
   :(LinearAlgebra.Transpose{<:Any,AT})            => (A,mut)->LinearAlgebra.transpose(mut(parent(A))),
   :(LinearAlgebra.LowerTriangular{<:Any,AT})      => (A,mut)->LinearAlgebra.LowerTriangular(mut(parent(A))),
@@ -39,7 +40,6 @@ const wrappers = (
   :(LinearAlgebra.UnitUpperTriangular{<:Any,AT})  => (A,mut)->LinearAlgebra.UnitUpperTriangular(mut(parent(A))),
   :(LinearAlgebra.Diagonal{<:Any,AT})             => (A,mut)->LinearAlgebra.Diagonal(mut(parent(A))),
   :(LinearAlgebra.Tridiagonal{<:Any,AT})          => (A,mut)->LinearAlgebra.Tridiagonal(mut(A.dl), mut(A.d), mut(A.du)),
-  :(Base.ReshapedArray{<:Any,<:Any,AT,<:Any})     => (A,mut)->Base.reshape(mut(parent(A)), size(A)),
 )
 
 permutation(::PermutedDimsArray{T,N,perm}) where {T,N,perm} = perm
diff --git a/test/runtests.jl b/test/runtests.jl
index 372e479..0383b46 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -45,14 +45,26 @@ Adapt.adapt_structure(to, xs::Wrapper) = Wrapper(adapt(to, xs.arr))
 @test adapt(CustomArray, (a=val.arr,)) == (a=val,)
 
 @test adapt(CustomArray, view(val.arr,:,:)) == view(val,:,:)
-@test adapt(CustomArray, view(val.arr,:,:)) isa SubArray{<:Any,<:Any,<:CustomArray}
+const inds = CustomArray{Int,1}([1,2])
+@test adapt(CustomArray, view(val.arr,inds.arr,:)) == view(val,inds,:)
+
+# NOTE: manual creation of PermutedDimsArray because permutedims collects
+@test adapt(CustomArray, PermutedDimsArray(val.arr,(2,1))) == PermutedDimsArray(val,(2,1))
 
 # NOTE: manual creation of ReshapedArray because Base.Array has an optimized `reshape`
 @test adapt(CustomArray, Base.ReshapedArray(val.arr,(2,2),())) == reshape(val,(2,2))
-@test adapt(CustomArray, Base.ReshapedArray(val.arr,(2,2),())) isa Base.ReshapedArray{<:Any,<:Any,<:CustomArray}
 
 
 using LinearAlgebra
 
 @test adapt(CustomArray, val.arr') == val'
-@test adapt(CustomArray, val.arr') isa Adjoint{<:Any,<:CustomArray}
+
+@test adapt(CustomArray, transpose(val.arr)) == transpose(val)
+
+@test adapt(CustomArray, LowerTriangular(val.arr)) == LowerTriangular(val)
+@test adapt(CustomArray, UnitLowerTriangular(val.arr)) == UnitLowerTriangular(val)
+@test adapt(CustomArray, UpperTriangular(val.arr)) == UpperTriangular(val)
+@test adapt(CustomArray, UnitUpperTriangular(val.arr)) == UnitUpperTriangular(val)
+
+@test adapt(CustomArray, Diagonal(val.arr)) == Diagonal(val)
+@test adapt(CustomArray, Tridiagonal(val.arr)) == Tridiagonal(val)