diff --git a/holoviews/core/data/grid.py b/holoviews/core/data/grid.py
index d7d9f5a25b..f61b0aa087 100644
--- a/holoviews/core/data/grid.py
+++ b/holoviews/core/data/grid.py
@@ -188,7 +188,7 @@ def groupby(cls, dataset, dim_names, container_type, group_type, **kwargs):
             group_kwargs['kdims'] = kdims
         group_kwargs.update(kwargs)
 
-        drop_dim = len(group_kwargs['kdims']) != len(kdims)
+        drop_dim = any(d not in group_kwargs['kdims'] for d in kdims)
 
         # Find all the keys along supplied dimensions
         keys = [dataset.data[d.name] for d in dimensions]
@@ -206,7 +206,7 @@ def groupby(cls, dataset, dim_names, container_type, group_type, **kwargs):
                 group_data = {dataset.vdims[0].name: np.atleast_1d(group_data)}
                 for dim, v in zip(dim_names, unique_key):
                     group_data[dim] = np.atleast_1d(v)
-            else:
+            elif not drop_dim:
                 for vdim in dataset.vdims:
                     group_data[vdim.name] = np.squeeze(group_data[vdim.name])
             group_data = group_type(group_data, **group_kwargs)
diff --git a/holoviews/core/data/iris.py b/holoviews/core/data/iris.py
index 1a0f409789..376b12dde2 100644
--- a/holoviews/core/data/iris.py
+++ b/holoviews/core/data/iris.py
@@ -117,7 +117,8 @@ def init(cls, eltype, data, kdims, vdims):
 
     @classmethod
     def validate(cls, dataset):
-        pass
+        if len(dataset.vdims) > 1:
+            raise ValueError("Iris cubes do not support more than one value dimension")
 
 
     @classmethod
@@ -187,7 +188,7 @@ def groupby(cls, dataset, dims, container_type=HoloMap, group_type=None, **kwarg
             group_kwargs['kdims'] = slice_dims
         group_kwargs.update(kwargs)
 
-        drop_dim = len(group_kwargs['kdims']) != len(slice_dims)
+        drop_dim = any(d not in group_kwargs['kdims'] for d in slice_dims)
 
         unique_coords = product(*[cls.values(dataset, d, expanded=False)
                                   for d in dims])
diff --git a/holoviews/core/data/xarray.py b/holoviews/core/data/xarray.py
index 4dbba497c3..90f5001e06 100644
--- a/holoviews/core/data/xarray.py
+++ b/holoviews/core/data/xarray.py
@@ -105,7 +105,7 @@ def groupby(cls, dataset, dimensions, container_type, group_type, **kwargs):
                                 kdims=element_dims)
         group_kwargs.update(kwargs)
 
-        drop_dim = len(group_kwargs['kdims']) != len(element_dims)
+        drop_dim = any(d not in group_kwargs['kdims'] for d in element_dims)
 
         # XArray 0.7.2 does not support multi-dimensional groupby
         # Replace custom implementation when 
diff --git a/tests/testdataset.py b/tests/testdataset.py
index 48e902041f..c5ea095d89 100644
--- a/tests/testdataset.py
+++ b/tests/testdataset.py
@@ -877,6 +877,22 @@ def test_dataset_groupby_drop_dims_dynamic(self):
             partial = ds.to(Dataset, kdims=['x'], vdims=['Val'], groupby='y', dynamic=True)
             self.assertEqual(partial[19]['Val'], array[:, -1, :].T.flatten())
 
+    def test_dataset_groupby_drop_dims_with_vdim(self):
+        array = np.random.rand(3, 20, 10)
+        ds = Dataset({'x': range(10), 'y': range(20), 'z': range(3), 'Val': array, 'Val2': array*2},
+                     kdims=['x', 'y', 'z'], vdims=['Val', 'Val2'])
+        with DatatypeContext([self.datatype, 'columns', 'dataframe']):
+            partial = ds.to(Dataset, kdims=['Val'], vdims=['Val2'], groupby='y')
+        self.assertEqual(partial.last['Val'], array[:, -1, :].T.flatten())
+
+    def test_dataset_groupby_drop_dims_dynamic_with_vdim(self):
+        array = np.random.rand(3, 20, 10)
+        ds = Dataset({'x': range(10), 'y': range(20), 'z': range(3), 'Val': array, 'Val2': array*2},
+                     kdims=['x', 'y', 'z'], vdims=['Val', 'Val2'])
+        with DatatypeContext([self.datatype, 'columns', 'dataframe']):
+            partial = ds.to(Dataset, kdims=['Val'], vdims=['Val2'], groupby='y', dynamic=True)
+            self.assertEqual(partial[19]['Val'], array[:, -1, :].T.flatten())
+
 
 class IrisDatasetTest(GridDatasetTest):
     """
@@ -929,6 +945,12 @@ def test_dataset_sample_hm(self):
     def test_dataset_sample_hm_alias(self):
         raise SkipTest("Not supported")
 
+    def test_dataset_groupby_drop_dims_with_vdim(self):
+        raise SkipTest("Not supported")
+
+    def test_dataset_groupby_drop_dims_dynamic_with_vdim(self):
+        raise SkipTest("Not supported")
+    
 
 class XArrayDatasetTest(GridDatasetTest):
     """