diff --git a/gtda/diagrams/_utils.py b/gtda/diagrams/_utils.py
index c02557d04..476e2d1f4 100644
--- a/gtda/diagrams/_utils.py
+++ b/gtda/diagrams/_utils.py
@@ -12,9 +12,12 @@ def _subdiagrams(X, homology_dimensions, remove_dim=False):
     list of homology dimensions. It is assumed that all diagrams in X contain
     the same number of points in each homology dimension."""
     n = len(X)
-    Xs = np.concatenate([X[X[:, :, 2] == dim].reshape(n, -1, 3)
-                         for dim in homology_dimensions],
-                        axis=1)
+    if len(homology_dimensions) == 1:
+        Xs = X[X[:, :, 2] == homology_dimensions[0]].reshape(n, -1, 3)
+    else:
+        Xs = np.concatenate([X[X[:, :, 2] == dim].reshape(n, -1, 3)
+                             for dim in homology_dimensions],
+                            axis=1)
     if remove_dim:
         Xs = Xs[:, :, :2]
     return Xs
diff --git a/gtda/diagrams/preprocessing.py b/gtda/diagrams/preprocessing.py
index 1d50be726..368dedbc0 100644
--- a/gtda/diagrams/preprocessing.py
+++ b/gtda/diagrams/preprocessing.py
@@ -314,18 +314,21 @@ class Filtering(BaseEstimator, TransformerMixin, PlotterMixin):
     """Filtering of persistence diagrams.
 
     Filtering a diagram means discarding all points [b, d, q] representing
-    topological features whose lifetime d - b is less than or equal to a
-    cutoff value. Technically, discarded points are replaced by points on the
-    diagonal (i.e. whose birth and death values coincide), which carry no
-    information.
+    non-trivial topological features whose lifetime d - b is less than or
+    equal to a cutoff value. Points on the diagonal (i.e. for which b and d
+    are equal) may still appear in the output for padding purposes, but carry
+    no information.
+
+    Input collections of persistence diagrams for this transformer must
+    satisfy certain requirements, see e.g. :meth:`fit`.
 
     Parameters
     ----------
     homology_dimensions : list, tuple, or None, optional, default: ``None``
         When set to ``None``, subdiagrams corresponding to all homology
-        dimensions seen in :meth:`fit` will be filtered.
-        Otherwise, it contains the homology dimensions (as non-negative
-        integers) at which filtering should occur.
+        dimensions seen in :meth:`fit` will be filtered. Otherwise, it contains
+        the homology dimensions (as non-negative integers) at which filtering
+        should occur.
 
     epsilon : float, optional, default: ``0.01``
         The cutoff value controlling the amount of filtering.
@@ -368,6 +371,9 @@ def fit(self, X, y=None):
             Input data. Array of persistence diagrams, each a collection of
             triples [b, d, q] representing persistent topological features
             through their birth (b), death (d) and homology dimension (q).
+            It is important that, for each possible homology dimension, the
+            number of triples for which q equals that homology dimension is
+            constants across the entries of `X`.
 
         y : None
             There is no need for a target in a transformer, yet the pipeline
@@ -399,6 +405,9 @@ def transform(self, X, y=None):
             Input data. Array of persistence diagrams, each a collection of
             triples [b, d, q] representing persistent topological features
             through their birth (b), death (d) and homology dimension (q).
+            It is important that, for each possible homology dimension, the
+            number of triples for which q equals that homology dimension is
+            constants across the entries of X.
 
         y : None
             There is no need for a target in a transformer, yet the pipeline
@@ -406,10 +415,10 @@ def transform(self, X, y=None):
 
         Returns
         -------
-        Xt : ndarray of shape (n_samples, n_features, 3)
+        Xt : ndarray of shape (n_samples, n_features_filtered, 3)
             Filtered persistence diagrams. Only the subdiagrams corresponding
             to dimensions in :attr:`homology_dimensions_` are filtered.
-            Discarded points are replaced by points on the diagonal.
+            ``n_features_filtered`` is less than or equal to ``n_features`.
 
         """
         check_is_fitted(self)