diff --git a/holoviews/core/data/grid.py b/holoviews/core/data/grid.py
index 215ce1a128..adbb16694d 100644
--- a/holoviews/core/data/grid.py
+++ b/holoviews/core/data/grid.py
@@ -88,7 +88,7 @@ def init(cls, eltype, data, kdims, vdims):
         for vdim in vdim_names:
             shape = data[vdim].shape
             error = DataError if len(shape) > 1 else ValueError
-            if (not expected and shape == (1,)) or len(set((shape,)+shapes)) == 1:
+            if (not expected and shape == (1,)) or (len(set((shape,)+shapes)) == 1 and len(shape) > 1):
                 # If empty or an irregular mesh
                 pass
             elif len(shape) != len(expected):
@@ -105,7 +105,7 @@ def init(cls, eltype, data, kdims, vdims):
 
     @classmethod
     def irregular(cls, dataset, dim):
-        return dataset.data[dim.name].ndim > 1
+        return dataset.data[dim.name if isinstance(dim, Dimension) else dim].ndim > 1
 
 
     @classmethod
@@ -273,7 +273,7 @@ def ndloc(cls, dataset, indices):
                 selected[kd.name] = coords
                 all_scalar = False
         for d in dataset.dimensions():
-            if d in dataset.kdims and cls.irregular(dataset, d):
+            if d in dataset.kdims and not cls.irregular(dataset, d):
                 continue
             arr = dataset.dimension_values(d, flat=False)
             if all_scalar and len(dataset.vdims) == 1:
@@ -392,7 +392,7 @@ def select(cls, dataset, selection_mask=None, **selection):
 
         indexed = cls.indexed(dataset, selection)
         full_selection = [(d, selection.get(d.name, selection.get(d.label)))
-                      for d in dimensions]
+                          for d in dimensions]
         data = {}
         value_select = []
         for (dim, ind) in full_selection:
diff --git a/holoviews/core/data/iris.py b/holoviews/core/data/iris.py
index caebdb26b4..96bd1fd10d 100644
--- a/holoviews/core/data/iris.py
+++ b/holoviews/core/data/iris.py
@@ -132,6 +132,12 @@ def validate(cls, dataset, vdims=True):
             raise DataError("Iris cubes do not support more than one value dimension", cls)
 
 
+    @classmethod
+    def irregular(cls, dataset, dim):
+        "CubeInterface does not support irregular data"
+        return False
+
+
     @classmethod
     def shape(cls, dataset, gridded=False):
         if gridded:
diff --git a/holoviews/core/data/xarray.py b/holoviews/core/data/xarray.py
index 2b55da53ba..ca1a4adb40 100644
--- a/holoviews/core/data/xarray.py
+++ b/holoviews/core/data/xarray.py
@@ -169,19 +169,20 @@ def groupby(cls, dataset, dimensions, container_type, group_type, **kwargs):
 
 
     @classmethod
-    def coords(cls, dataset, dim, ordered=False, expanded=False, edges=False):
-        dim = dataset.get_dimension(dim, strict=True)
+    def coords(cls, dataset, dimension, ordered=False, expanded=False, edges=False):
+        dim = dataset.get_dimension(dimension)
+        dim = dimension if dim is None else dim.name
         irregular = cls.irregular(dataset, dim)
         if irregular or expanded:
             if irregular:
-                data = dataset.data[dim.name]
+                data = dataset.data[dim]
             else:
                 data = util.expand_grid_coords(dataset, dim)
             if edges:
                 data = cls._infer_interval_breaks(data, axis=1)
                 data = cls._infer_interval_breaks(data, axis=0)
             return data
-        data = np.atleast_1d(dataset.data[dim.name].data)
+        data = np.atleast_1d(dataset.data[dim].data)
         if ordered and data.shape and np.all(data[1:] < data[:-1]):
             data = data[::-1]
         return data
@@ -191,12 +192,12 @@ def coords(cls, dataset, dim, ordered=False, expanded=False, edges=False):
     def values(cls, dataset, dim, expanded=True, flat=True):
         dim = dataset.get_dimension(dim, strict=True)
         data = dataset.data[dim.name].data
-        irregular = cls.irregular(dataset, dim)
+        irregular = cls.irregular(dataset, dim) if dim in dataset.kdims else False
         if dim in dataset.vdims or irregular:
             coord_dims = list(dataset.data[dim.name].dims)
             if dask and isinstance(data, dask.array.Array):
                 data = data.compute()
-            if not irregular:
+            if not irregular and not any(cls.irregular(dataset, d) for d in dataset.kdims):
                 data = cls.canonicalize(dataset, data, coord_dims=coord_dims)
             return data.T.flatten() if flat else data
         elif expanded:
@@ -226,18 +227,18 @@ def unpack_scalar(cls, dataset, data):
 
     @classmethod
     def ndloc(cls, dataset, indices):
-        kdims = [d.name for d in dataset.kdims[::-1]]
+        kdims = [d for d in dataset.kdims[::-1]]
         adjusted_indices = []
         slice_dims = []
         for kd, ind in zip(kdims, indices):
-            if dataset.data[kd].ndim > 1:
+            if cls.irregular(dataset, kd):
                 coords = [c for c in dataset.data.coords if c not in dataset.data.dims]
-                dim = dataset.data[kd].dims[coords.index(kd)]
-                shape = dataset.data[kd].shape[coords.index(kd)]
+                dim = dataset.data[kd.name].dims[coords.index(kd.name)]
+                shape = dataset.data[kd.name].shape[coords.index(kd.name)]
                 coords = np.arange(shape)
             else:
                 coords = cls.coords(dataset, kd, False)
-                dim = kd
+                dim = kd.name
             slice_dims.append(dim)
             ncoords = len(coords)
             if np.all(coords[1:] < coords[:-1]):