diff --git a/src/word-list.c b/src/word-list.c
index a88fe93ad17ccf03308151f0e214cb80093a00ea..42b993066f6ea6299d9cbf178c8d2e0e37eafa2a 100644
--- a/src/word-list.c
+++ b/src/word-list.c
@@ -1393,8 +1393,8 @@ word_list_find_intersection (WordList     *word_list,
 {
   guint n_chars1 = 0;
   guint n_chars2 = 0;
-  g_autoptr (IpuzCharset) charset1 = NULL;
-  g_autoptr (IpuzCharset) charset2 = NULL;
+  g_autoptr (IpuzCharset) charset_incomplete = NULL;
+  g_autoptr (IpuzCharset) charset_complete = NULL;
   gboolean filter1_valid = FALSE;
   gboolean filter2_valid = FALSE;
   gunichar c1 = 0;
@@ -1467,64 +1467,71 @@ word_list_find_intersection (WordList     *word_list,
     {
       if (filter1_valid)
         {
-          charset1 = calculate_intersect_phase2 (word_list,
-                                                 filter1, pos1,
-                                                 n_chars1,
-                                                 NULL,
-                                                 word_array1?*word_array1:NULL);
+          charset_complete =
+            calculate_intersect_phase2 (word_list,
+                                        filter1, pos1,
+                                        n_chars1,
+                                        NULL,
+                                        word_array1?*word_array1:NULL);
           if (intersecting_chars)
-            *intersecting_chars = ipuz_charset_ref (charset1);
+            *intersecting_chars = ipuz_charset_ref (charset_complete);
           sort_word_arrays (word_array1, word_array2);
         }
       else if (filter2_valid)
         {
-          charset2 = calculate_intersect_phase2 (word_list,
-                                                 filter2, pos2,
-                                                 n_chars2,
-                                                 NULL,
-                                                 word_array2?*word_array2:NULL);
+          charset_complete =
+            calculate_intersect_phase2 (word_list,
+                                        filter2, pos2,
+                                        n_chars2,
+                                        NULL,
+                                        word_array2?*word_array2:NULL);
           if (intersecting_chars)
-            *intersecting_chars = ipuz_charset_ref (charset2);
+            *intersecting_chars = ipuz_charset_ref (charset_complete);
           sort_word_arrays (word_array1, word_array2);
         }
-
       return;
     }
 
 
   /* Both filter1 and filter2 are valid, so we have to calculate the
-   * intersections. This is done in three phases.
-   */
-
-  /* Phase 1: Calculate the set of possible characters at pos1 for
-   * filter1. We don't need to worry about calculating the word_list
-   * yet */
-  charset1 = calculate_intersect_phase1 (word_list,
-                                         filter1, pos1,
-                                         n_chars1);
-
-  /* phase 2: Calculate the overlapping characters and the second
-   * word_array. If necessary, calculate the second filters word_array */
-  charset2 =
+   * intersections. This is done in three phases. */
+
+  /* Phase 1: Calculate the set of possible characters at pos2 of
+   * the second clue, constrained by the second clue's filter. */
+  charset_incomplete = calculate_intersect_phase1 (word_list,
+                                                   filter2,
+                                                   pos2,
+                                                   n_chars2);
+
+  /* Phase 2: Calculate the set of possible characters at pos1 of
+   * the first clue, constrained by the first clue's filter, and by
+   * charset_incomplete. If necessary, calculate word_array1. */
+  charset_complete =
     calculate_intersect_phase2 (word_list,
-                                filter2, pos2,
-                                n_chars2,
-                                charset1,
-                                word_array2?*word_array2:NULL);
-
-  /* phase 3: Recalculate the word_array first filter with the
-   * overlap */
-  calculate_intersect_phase3 (word_list,
-                              filter1, pos1,
-                              n_chars1,
-                              charset2,
-                              word_array1?*word_array1:NULL);
+                                filter1,
+                                pos1,
+                                n_chars1,
+                                charset_incomplete,
+                                word_array1?*word_array1:NULL);
+
+  /* Phase 3 (optional): Calculate the set of possible characters at
+   * pos2 of the second clue, constrained by the second clue's filter,
+   * and by charset_complete. Calculate word_array2. */
+  if (word_array2 != NULL)
+    {
+      calculate_intersect_phase3 (word_list,
+                                  filter2,
+                                  pos2,
+                                  n_chars2,
+                                  charset_complete,
+                                  *word_array2);
+    }
 
   sort_word_arrays (word_array1, word_array2);
 
   /* copy our charset over to intersecting_chars */
   if (intersecting_chars)
-    *intersecting_chars = ipuz_charset_ref (charset2);
+    *intersecting_chars = ipuz_charset_ref (charset_complete);
 
   PUSH_TIMER ("word_list_find_intersection()");
 }
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