diff --git a/gem/gem.py b/gem/gem.py
index 974556754..f3cf45900 100644
--- a/gem/gem.py
+++ b/gem/gem.py
@@ -985,10 +985,10 @@ def __new__(cls, i, j, dtype=None):
         if isinstance(i, Integral) and isinstance(j, Integral):
             return one if i == j else Zero()
 
-        if isinstance(i, Integral):
+        if isinstance(i, Integral) and not isinstance(j, Index):
             return Indexed(Literal(numpy.eye(j.extent)[i]), (j,))
 
-        if isinstance(j, Integral):
+        if isinstance(j, Integral) and not isinstance(i, Index):
             return Indexed(Literal(numpy.eye(i.extent)[j]), (i,))
 
         self = super(Delta, cls).__new__(cls)