diff --git a/src/abstract.jl b/src/abstract.jl
index c3940a3..2f33b0f 100644
--- a/src/abstract.jl
+++ b/src/abstract.jl
@@ -179,6 +179,23 @@ storage_type(op::Adjoint) = storage_type(parent(op))
 storage_type(op::Transpose) = storage_type(parent(op))
 storage_type(op::Diagonal) = typeof(parent(op))
 
+@inline function _select_storage_type(
+  op1::AbstractLinearOperator,
+  op2::AbstractLinearOperator,
+  T::Type,
+)
+  S = promote_type(storage_type(op1), storage_type(op2))
+  if isconcretetype(S)
+    return S
+  elseif isconcretetype(storage_type(op1))
+    return storage_type(op1)
+  elseif isconcretetype(storage_type(op2))
+    return storage_type(op2)
+  else
+    return Vector{T}
+  end
+end
+
 """
   reset!(op)
 
diff --git a/src/cat.jl b/src/cat.jl
index 764c789..b20e1be 100644
--- a/src/cat.jl
+++ b/src/cat.jl
@@ -45,9 +45,7 @@ function hcat(A::AbstractLinearOperator, B::AbstractLinearOperator)
   ctprod! = @closure (res, w, α, β) ->
     hcat_ctprod!(res, adjoint(A), adjoint(B), Ancol, Ancol + Bncol, w, α, β)
   args5 = (has_args5(A) && has_args5(B))
-  S = promote_type(storage_type(A), storage_type(B))
-  isconcretetype(S) ||
-    throw(LinearOperatorException("storage types cannot be promoted to a concrete type"))
+  S = _select_storage_type(A, B, T)
   CompositeLinearOperator(T, nrow, ncol, false, false, prod!, tprod!, ctprod!, args5, S = S)
 end
 
@@ -104,9 +102,7 @@ function vcat(A::AbstractLinearOperator, B::AbstractLinearOperator)
   ctprod! = @closure (res, w, α, β) ->
     vcat_ctprod!(res, adjoint(A), adjoint(B), Anrow, Anrow + Bnrow, w, α, β)
   args5 = (has_args5(A) && has_args5(B))
-  S = promote_type(storage_type(A), storage_type(B))
-  isconcretetype(S) ||
-    throw(LinearOperatorException("storage types cannot be promoted to a concrete type"))
+  S = _select_storage_type(A, B, T)
   CompositeLinearOperator(T, nrow, ncol, false, false, prod!, tprod!, ctprod!, args5, S = S)
 end
 
diff --git a/src/operations.jl b/src/operations.jl
index 18259d4..b02803d 100644
--- a/src/operations.jl
+++ b/src/operations.jl
@@ -139,9 +139,7 @@ function *(op1::AbstractLinearOperator, op2::AbstractLinearOperator)
   if m2 != n1
     throw(LinearOperatorException("shape mismatch"))
   end
-  S = promote_type(storage_type(op1), storage_type(op2))
-  isconcretetype(S) ||
-    throw(LinearOperatorException("storage types cannot be promoted to a concrete type"))
+  S = _select_storage_type(op1, op2, T)
   #tmp vector for products
   vtmp = fill!(S(undef, m2), zero(T))
   utmp = fill!(S(undef, n1), zero(T))
@@ -210,9 +208,7 @@ function +(op1::AbstractLinearOperator, op2::AbstractLinearOperator)
   symm = (issymmetric(op1) && issymmetric(op2))
   herm = (ishermitian(op1) && ishermitian(op2))
   args5 = (has_args5(op1) && has_args5(op2))
-  S = promote_type(storage_type(op1), storage_type(op2))
-  isconcretetype(S) ||
-    throw(LinearOperatorException("storage types cannot be promoted to a concrete type"))
+  S = _select_storage_type(op1, op2, T)
   return CompositeLinearOperator(T, m1, n1, symm, herm, prod!, tprod!, ctprod!, args5, S = S)
 end