diff --git a/src/symmetric.jl b/src/symmetric.jl
index ed5fe3b5..061abb49 100644
--- a/src/symmetric.jl
+++ b/src/symmetric.jl
@@ -289,7 +289,7 @@ Base.dataids(A::HermOrSym) = Base.dataids(parent(A))
 Base.unaliascopy(A::Hermitian) = Hermitian(Base.unaliascopy(parent(A)), sym_uplo(A.uplo))
 Base.unaliascopy(A::Symmetric) = Symmetric(Base.unaliascopy(parent(A)), sym_uplo(A.uplo))
 
-_conjugation(::Union{Symmetric, Hermitian{<:Real}}) = transpose
+_conjugation(::Symmetric) = transpose
 _conjugation(::Hermitian) = adjoint
 
 diag(A::Symmetric) = symmetric.(diag(parent(A)), sym_uplo(A.uplo))
@@ -470,25 +470,25 @@ Base.conj!(A::HermOrSym) = typeof(A)(parentof_applytri(conj!, A), A.uplo)
 # tril/triu
 function tril(A::Hermitian, k::Integer=0)
     if A.uplo == 'U' && k <= 0
-        return tril!(copy(A.data'),k)
+        return tril_maybe_inplace(copy(A.data'),k)
     elseif A.uplo == 'U' && k > 0
-        return tril!(copy(A.data'),-1) + tril!(triu(A.data),k)
+        return tril_maybe_inplace(copy(A.data'),-1) + tril_maybe_inplace(triu(A.data),k)
     elseif A.uplo == 'L' && k <= 0
         return tril(A.data,k)
     else
-        return tril(A.data,-1) + tril!(triu!(copy(A.data')),k)
+        return tril(A.data,-1) + tril_maybe_inplace(triu_maybe_inplace(copy(A.data')),k)
     end
 end
 
 function tril(A::Symmetric, k::Integer=0)
     if A.uplo == 'U' && k <= 0
-        return tril!(copy(transpose(A.data)),k)
+        return tril_maybe_inplace(copy(transpose(A.data)),k)
     elseif A.uplo == 'U' && k > 0
-        return tril!(copy(transpose(A.data)),-1) + tril!(triu(A.data),k)
+        return tril_maybe_inplace(copy(transpose(A.data)),-1) + tril_maybe_inplace(triu(A.data),k)
     elseif A.uplo == 'L' && k <= 0
         return tril(A.data,k)
     else
-        return tril(A.data,-1) + tril!(triu!(copy(transpose(A.data))),k)
+        return tril(A.data,-1) + tril_maybe_inplace(triu_maybe_inplace(copy(transpose(A.data))),k)
     end
 end
 
@@ -496,11 +496,11 @@ function triu(A::Hermitian, k::Integer=0)
     if A.uplo == 'U' && k >= 0
         return triu(A.data,k)
     elseif A.uplo == 'U' && k < 0
-        return triu(A.data,1) + triu!(tril!(copy(A.data')),k)
+        return triu(A.data,1) + triu_maybe_inplace(tril_maybe_inplace(copy(A.data')),k)
     elseif A.uplo == 'L' && k >= 0
-        return triu!(copy(A.data'),k)
+        return triu_maybe_inplace(copy(A.data'),k)
     else
-        return triu!(copy(A.data'),1) + triu!(tril(A.data),k)
+        return triu_maybe_inplace(copy(A.data'),1) + triu_maybe_inplace(tril(A.data),k)
     end
 end
 
@@ -508,11 +508,11 @@ function triu(A::Symmetric, k::Integer=0)
     if A.uplo == 'U' && k >= 0
         return triu(A.data,k)
     elseif A.uplo == 'U' && k < 0
-        return triu(A.data,1) + triu!(tril!(copy(transpose(A.data))),k)
+        return triu(A.data,1) + triu_maybe_inplace(tril_maybe_inplace(copy(transpose(A.data))),k)
     elseif A.uplo == 'L' && k >= 0
-        return triu!(copy(transpose(A.data)),k)
+        return triu_maybe_inplace(copy(transpose(A.data)),k)
     else
-        return triu!(copy(transpose(A.data)),1) + triu!(tril(A.data),k)
+        return triu_maybe_inplace(copy(transpose(A.data)),1) + triu_maybe_inplace(tril(A.data),k)
     end
 end
 
diff --git a/src/triangular.jl b/src/triangular.jl
index 5b476d24..906a25aa 100644
--- a/src/triangular.jl
+++ b/src/triangular.jl
@@ -484,6 +484,11 @@ function tril!(A::UnitLowerTriangular, k::Integer=0)
     return tril!(LowerTriangular(A.data), k)
 end
 
+tril_maybe_inplace(A, k::Integer=0) = tril(A, k)
+triu_maybe_inplace(A, k::Integer=0) = triu(A, k)
+tril_maybe_inplace(A::StridedMatrix, k::Integer=0) = tril!(A, k)
+triu_maybe_inplace(A::StridedMatrix, k::Integer=0) = triu!(A, k)
+
 adjoint(A::LowerTriangular) = UpperTriangular(adjoint(A.data))
 adjoint(A::UpperTriangular) = LowerTriangular(adjoint(A.data))
 adjoint(A::UnitLowerTriangular) = UnitUpperTriangular(adjoint(A.data))
diff --git a/test/symmetric.jl b/test/symmetric.jl
index 9f727b8c..5de3a853 100644
--- a/test/symmetric.jl
+++ b/test/symmetric.jl
@@ -1199,4 +1199,27 @@ end
     end
 end
 
+@testset "triu/tril with immutable arrays" begin
+    struct ImmutableMatrix{T,A<:AbstractMatrix{T}} <: AbstractMatrix{T}
+        a :: A
+    end
+    Base.size(A::ImmutableMatrix) = size(A.a)
+    Base.getindex(A::ImmutableMatrix, i::Int, j::Int) = getindex(A.a, i, j)
+    Base.copy(A::ImmutableMatrix) = A
+    LinearAlgebra.adjoint(A::ImmutableMatrix) = ImmutableMatrix(adjoint(A.a))
+    LinearAlgebra.transpose(A::ImmutableMatrix) = ImmutableMatrix(transpose(A.a))
+
+    A = ImmutableMatrix([1 2; 3 4])
+    for T in (Symmetric, Hermitian), uplo in (:U, :L)
+        H = T(A, uplo)
+        MH = Matrix(H)
+        @test triu(H,-1) == triu(MH,-1)
+        @test triu(H) == triu(MH)
+        @test triu(H,1) == triu(MH,1)
+        @test tril(H,1) == tril(MH,1)
+        @test tril(H) == tril(MH)
+        @test tril(H,-1) == tril(MH,-1)
+    end
+end
+
 end # module TestSymmetric