diff --git a/gpytorch/lazy/lazy_evaluated_kernel_tensor.py b/gpytorch/lazy/lazy_evaluated_kernel_tensor.py
index 610a15ad0..3efe398b4 100644
--- a/gpytorch/lazy/lazy_evaluated_kernel_tensor.py
+++ b/gpytorch/lazy/lazy_evaluated_kernel_tensor.py
@@ -161,7 +161,7 @@ def _getitem(self, row_index, col_index, *batch_indices):
         # However - if we have multiple outputs per input, then the indices won't directly
         # correspond to the entries of row/col. We'll have to do a little pre-processing
         if num_outs_per_in_rows != 1 or num_outs_per_in_cols != 1:
-            if not isinstance(x1, slice) or not isinstance(x2, slice):
+            if not isinstance(row_index, slice) or not isinstance(col_index, slice):
                 # It's too complicated to deal with tensor indices in this case - we'll use the super method
                 return self.evaluate_kernel()._getitem(row_index, col_index, *batch_indices)
 
@@ -169,13 +169,13 @@ def _getitem(self, row_index, col_index, *batch_indices):
             # Let's make sure that the slice dimensions perfectly correspond with the number of
             # outputs per input that we have
             row_start, row_end, row_step = (
-                row_index.start,
-                row_index.stop,
+                row_index.start or 0,
+                row_index.stop or self.shape[-2],
                 row_index.step,
             )
             col_start, col_end, col_step = (
-                col_index.start,
-                col_index.stop,
+                col_index.start or 0,
+                col_index.stop or self.shape[-1],
                 col_index.step,
             )
             if row_step is not None or col_step is not None:
diff --git a/test/lazy/test_lazy_evaluated_kernel_tensor.py b/test/lazy/test_lazy_evaluated_kernel_tensor.py
index 06d937d0c..7bb9e00af 100644
--- a/test/lazy/test_lazy_evaluated_kernel_tensor.py
+++ b/test/lazy/test_lazy_evaluated_kernel_tensor.py
@@ -122,6 +122,18 @@ def test_batch_getitem(self):
         self.assertEqual(k.size(), torch.Size([2, 5, 5]))
         self.assertEqual(k[..., :4, :3].size(), torch.Size([2, 4, 3]))
 
+    def test_batch_getitem_multioutput(self):
+        """Ensure slicing is efficient when using a multioutput kernel"""
+        x1 = torch.randn(5, 6)
+        x2 = torch.randn(5, 6)
+        kern = gpytorch.kernels.RBFKernelGrad(batch_shape=torch.Size([2]))
+        k = kern(x1, x2)
+        k.evaluate_kernel = MagicMock(name="evaluate_kernel")
+        k_sliced = k[..., :7, :14]
+        self.assertFalse(k.evaluate_kernel.called)
+        self.assertEqual(k.size(), torch.Size([2, 35, 35]))
+        self.assertEqual(k_sliced.size(), torch.Size([2, 7, 14]))
+
     def test_getitem_tensor_index(self):
         # Not supported a.t.m. with LazyEvaluatedKernelTensors
         pass