diff --git a/src/TiledArray/einsum/tiledarray.h b/src/TiledArray/einsum/tiledarray.h
index 52dab7477e..09640d31f6 100644
--- a/src/TiledArray/einsum/tiledarray.h
+++ b/src/TiledArray/einsum/tiledarray.h
@@ -309,7 +309,7 @@ auto einsum(expressions::TsrExpr<ArrayT_> A, expressions::TsrExpr<ArrayToT_> B,
   Einsum::Index<std::string> c = std::get<0>(cs);
 
   struct {
-    std::string a, b, c;
+    std::string b, c;
   } inner;
   if constexpr (std::tuple_size<decltype(cs)>::value == 2) {
     inner.b = ";" + (std::string)std::get<1>(Einsum::idx(B));
@@ -319,16 +319,13 @@ auto einsum(expressions::TsrExpr<ArrayT_> A, expressions::TsrExpr<ArrayToT_> B,
   // these are "Hadamard" (fused) indices
   auto h = a & b & c;
 
-  auto e = (a ^ b);
   // contracted indices
   auto i = (a & b) - h;
+  // contraction not allowed in tensor x tensor-of-tensor
+  TA_ASSERT(!i);
 
-  // cannot be hadamard reduction type operation for this overload
-  TA_ASSERT(e);
-
-  // no Hadamard indices => standard contraction (or even outer product)
-  // same a, b, and c => pure Hadamard
-  TA_ASSERT(!h || (!(a ^ b) && !(b ^ c)));
+  // indices exclusively in 'a' or exclusively in 'b'
+  auto e = (a ^ b);
 
   // maps Index to TiledRange1
   // (asserts same index maps to the same TR1 in A, and B)
@@ -364,6 +361,9 @@ auto einsum(expressions::TsrExpr<ArrayT_> A, expressions::TsrExpr<ArrayToT_> B,
   }
   C.expr = e;
 
+  arrayTermB.expr += inner.b;
+  C.expr += inner.c;
+
   struct {
     RangeProduct tiles;
     std::vector<std::vector<size_t>> batch;
@@ -453,7 +453,10 @@ auto einsum(expressions::TsrExpr<ArrayT_> A, expressions::TsrExpr<ArrayToT_> B,
     }
 
     // todo
-    // C.ei(C.expr) = (A.ei(A.expr) * B.ei(B.expr)).set_world(*owners);
+    C.ei(C.expr) = (A.ei(A.expr) * B.ei(B.expr)).set_world(*owners);
+
+    //
+
     A.ei.defer_deleter_to_next_fence();
     B.ei.defer_deleter_to_next_fence();
     A.ei = ArrayT();
diff --git a/src/TiledArray/expressions/binary_engine.h b/src/TiledArray/expressions/binary_engine.h
index 4758ab0069..93192e2b5e 100644
--- a/src/TiledArray/expressions/binary_engine.h
+++ b/src/TiledArray/expressions/binary_engine.h
@@ -146,11 +146,10 @@ class BinaryEngine : public ExprEngine<Derived> {
         TiledArray::detail::is_tensor_of_tensor_v<left_tile_type>;
     constexpr bool right_tile_is_tot =
         TiledArray::detail::is_tensor_of_tensor_v<right_tile_type>;
-    static_assert(!(left_tile_is_tot ^ right_tile_is_tot),
-                  "ContEngine can only handle tensors of same nested-ness "
-                  "(both plain or both ToT)");
     constexpr bool args_are_plain_tensors =
         !left_tile_is_tot && !right_tile_is_tot;
+    constexpr bool args_are_mixed_tensors =
+        left_tile_is_tot ^ right_tile_is_tot;
     if (args_are_plain_tensors &&
         (left_outer_permtype_ == PermutationType::matrix_transpose ||
          left_outer_permtype_ == PermutationType::identity)) {
@@ -175,6 +174,20 @@ class BinaryEngine : public ExprEngine<Derived> {
           right_inner_permtype_ == PermutationType::identity))) {
       right_.permute_tiles(false);
     }
+    if (args_are_mixed_tensors &&
+        ((left_outer_permtype_ == PermutationType::matrix_transpose ||
+          left_outer_permtype_ == PermutationType::identity) ||
+         (left_inner_permtype_ == PermutationType::matrix_transpose ||
+          left_inner_permtype_ == PermutationType::identity))) {
+      left_.permute_tiles(false);
+    }
+    if (args_are_mixed_tensors &&
+        ((left_outer_permtype_ == PermutationType::matrix_transpose ||
+          left_outer_permtype_ == PermutationType::identity) ||
+         (right_inner_permtype_ == PermutationType::matrix_transpose ||
+          right_inner_permtype_ == PermutationType::identity))) {
+      right_.permute_tiles(false);
+    }
   }
 
  public: