diff --git a/spacy_experimental/coref/coref_component.py b/spacy_experimental/coref/coref_component.py
index 1e6788d..38ee7c1 100644
--- a/spacy_experimental/coref/coref_component.py
+++ b/spacy_experimental/coref/coref_component.py
@@ -145,6 +145,11 @@ def predict(self, docs: Iterable[Doc]) -> List[MentionClusters]:
         """
         out = []
         for doc in docs:
+            if len(doc) < 2:
+                # no coref in docs with 0 or 1 token
+                out.append([])
+                continue
+
             scores, idxs = self.model.predict([doc])
             # idxs is a list of mentions (start / end idxs)
             # each item in scores includes scores and a mapping from scores to mentions
@@ -232,6 +237,9 @@ def update(
                     predicted docs in coref training.
                     """
                 )
+            if len(eg.predicted) < 2:
+                # no prediction possible for docs of length 0 or 1
+                continue
             preds, backprop = self.model.begin_update([eg.predicted])
             score_matrix, mention_idx = preds
             loss, d_scores = self.get_loss([eg], score_matrix, mention_idx)
diff --git a/spacy_experimental/coref/tests/test_coref.py b/spacy_experimental/coref/tests/test_coref.py
index 6ff07d4..31caf9a 100644
--- a/spacy_experimental/coref/tests/test_coref.py
+++ b/spacy_experimental/coref/tests/test_coref.py
@@ -37,6 +37,11 @@ def generate_train_data(prefix=DEFAULT_CLUSTER_PREFIX):
                 }
             },
         ),
+        (
+            # example short doc
+            "ok",
+            {"spans": {}}
+        )
     ]
     # fmt: on
     return data
@@ -83,11 +88,12 @@ def test_initialized(nlp):
 
 
 def test_initialized_short(nlp):
+    # test that short or empty docs don't fail
     nlp.add_pipe("experimental_coref")
     nlp.initialize()
     assert nlp.pipe_names == ["experimental_coref"]
-    text = "Hi there"
-    doc = nlp(text)
+    doc = nlp("Hi")
+    doc = nlp("")
 
 
 def test_coref_serialization(nlp):
@@ -148,7 +154,8 @@ def test_overfitting_IO(nlp, train_data):
 
 def test_tokenization_mismatch(nlp, train_data):
     train_examples = []
-    for text, annot in train_data:
+    # this is testing a specific test example, so just get the first doc
+    for text, annot in train_data[0:1]:
         eg = Example.from_dict(nlp.make_doc(text), annot)
         ref = eg.reference
         char_spans = {}
diff --git a/spacy_experimental/coref/tests/test_span_resolver.py b/spacy_experimental/coref/tests/test_span_resolver.py
index d2d829d..e0238ee 100644
--- a/spacy_experimental/coref/tests/test_span_resolver.py
+++ b/spacy_experimental/coref/tests/test_span_resolver.py
@@ -79,6 +79,13 @@ def test_not_initialized(nlp):
     with pytest.raises(ValueError, match="E109"):
         nlp(text)
 
+def test_initialized_short(nlp):
+    # docs with one or no tokens should not fail
+    nlp.add_pipe("experimental_span_resolver")
+    nlp.initialize()
+    assert nlp.pipe_names == ["experimental_span_resolver"]
+    nlp("hi")
+    nlp("")
 
 def test_span_resolver_serialization(nlp):
     # Test that the span resolver component can be serialized