diff --git a/docs/api.md b/docs/api.md
index 656a94f..2299a21 100644
--- a/docs/api.md
+++ b/docs/api.md
@@ -211,12 +211,13 @@ The code-entry Helper object has the following API:
   `get_word_completions("pr")` will return `{"ocessor", "ovincial",
   "oximate"}`, while `get_word_completions("opulent-pr")` will return
   `{"eclude", "efer", "eshrunk", "inter", "owler"}`. If the wordlist is not
-  yet known, this returns an empty set. It will also return an empty set if
-  the prefix is complete (the last word matches something in the completion
-  list, and there are no longer extension words), although the code may not
-  yet be complete if there are additional words. The completions will never
-  include a hyphen: the UI frontend must supply these if desired. The
-  frontend is also responsible for sorting the results before display.
+  yet known, this returns an empty set. It will include an empty string in
+  the returned set if the prefix is complete (the last word is an exact match
+  for something in the completion list), but will include additional strings
+  if the completion list includes extensions of the last word. The
+  completions will never include a hyphen: the UI frontend must supply these
+  if desired. The frontend is also responsible for sorting the results before
+  display.
 * `h.choose_words(words)`: call this when the user is finished typing in the
   code. It does not return anything, but will cause the Wormhole's
   `w.when_code()` (or corresponding delegate) to fire, and triggers the
diff --git a/src/wormhole/_wordlist.py b/src/wormhole/_wordlist.py
index 71d3f1a..3da0e15 100644
--- a/src/wormhole/_wordlist.py
+++ b/src/wormhole/_wordlist.py
@@ -167,7 +167,7 @@ class PGPWordList(object):
         lp = len(last_partial_word)
         completions = set()
         for word in words:
-            if word.startswith(prefix):
+            if word.startswith(last_partial_word):
                 completions.add(word[lp:])
         return completions
 
diff --git a/src/wormhole/test/test_wordlist.py b/src/wormhole/test/test_wordlist.py
new file mode 100644
index 0000000..56cac4b
--- /dev/null
+++ b/src/wormhole/test/test_wordlist.py
@@ -0,0 +1,20 @@
+from __future__ import print_function, unicode_literals
+import mock
+from twisted.trial import unittest
+from .._wordlist import PGPWordList
+
+class Completions(unittest.TestCase):
+    def test_completions(self):
+        wl = PGPWordList()
+        gc = wl.get_completions
+        self.assertEqual(gc("ar"), {"mistice", "ticle"})
+        self.assertEqual(gc("armis"), {"tice"})
+        self.assertEqual(gc("armistice-ba"),
+                         {"boon", "ckfield", "ckward", "njo"})
+        self.assertEqual(gc("armistice-baboon"), {""})
+
+class Choose(unittest.TestCase):
+    def test_choose_words(self):
+        wl = PGPWordList()
+        with mock.patch("os.urandom", side_effect=[b"\x04", b"\x10"]):
+            self.assertEqual(wl.choose_words(2), "alkali-assume")