diff --git a/src/index_notation/transformations.cpp b/src/index_notation/transformations.cpp
index f0728ef2b..5310455f6 100644
--- a/src/index_notation/transformations.cpp
+++ b/src/index_notation/transformations.cpp
@@ -1114,16 +1114,19 @@ static IndexStmt optimizeSpMM(IndexStmt stmt) {
     return stmt;
   }
 
+  // I think we can to linear combination of rows as long as there are no permutations in the format and the
+  // level formats are ordered. The i -> k -> j loops should iterate over the data structures without issue.
   TensorVar B = Baccess.getTensorVar();
-  if (B.getFormat().getModeOrdering()[0] != 0 ||
+  if (!B.getFormat().getModeFormats()[0].isOrdered() ||
+      !B.getFormat().getModeFormats()[1].isOrdered() ||
+      B.getFormat().getModeOrdering()[0] != 0 ||
       B.getFormat().getModeOrdering()[1] != 1) {
     return stmt;
   }
 
-  // We need random access into the first mode or this tensor in order to perform a linear combination of rows
-  // algorithm. (I think?)
   TensorVar C = Caccess.getTensorVar();
-  if (!C.getFormat().getModeFormats()[0].hasLocate() ||
+  if (!C.getFormat().getModeFormats()[0].isOrdered() ||
+      !C.getFormat().getModeFormats()[1].isOrdered() ||
       C.getFormat().getModeOrdering()[0] != 0 ||
       C.getFormat().getModeOrdering()[1] != 1) {
     return stmt;