diff --git a/spacy/tests/doc/test_doc_api.py b/spacy/tests/doc/test_doc_api.py
index f00668d83..ee99897d6 100644
--- a/spacy/tests/doc/test_doc_api.py
+++ b/spacy/tests/doc/test_doc_api.py
@@ -278,10 +278,30 @@ def test_doc_api_similarity_match():
     assert doc.similarity(doc2) == 0.0
 
 
-def test_lowest_common_ancestor(en_tokenizer):
-    tokens = en_tokenizer('the lazy dog slept')
-    doc = get_doc(tokens.vocab, [t.text for t in tokens], heads=[2, 1, 1, 0])
+@pytest.mark.parametrize('sentence,heads,lca_matrix', [
+    ('the lazy dog slept',
+     [2, 1, 1, 0],
+     numpy.array([[0, 2, 2, 3],
+                  [2, 1, 2, 3],
+                  [2, 2, 2, 3],
+                  [3, 3, 3, 3]])),
+    ('The lazy dog slept. The quick fox jumped',
+     [2, 1, 1, 0, -1, 2, 1, 1, 0],
+     numpy.array([[0, 2, 2, 3, 3, -1, -1, -1, -1],
+                  [2, 1, 2, 3, 3, -1, -1, -1, -1],
+                  [2, 2, 2, 3, 3, -1, -1, -1, -1],
+                  [3, 3, 3, 3, 3, -1, -1, -1, -1],
+                  [3, 3, 3, 3, 4, -1, -1, -1, -1],
+                  [-1, -1, -1, -1, -1, 5, 7, 7, 8],
+                  [-1, -1, -1, -1, -1, 7, 6, 7, 8],
+                  [-1, -1, -1, -1, -1, 7, 7, 7, 8],
+                  [-1, -1, -1, -1, -1, 8, 8, 8, 8]]))
+])
+def test_lowest_common_ancestor(en_tokenizer, sentence, heads, lca_matrix):
+    tokens = en_tokenizer(sentence)
+    doc = get_doc(tokens.vocab, [t.text for t in tokens], heads=heads)
     lca = doc.get_lca_matrix()
+    assert (lca == lca_matrix).all()
     assert(lca[1, 1] == 1)
     assert(lca[0, 1] == 2)
     assert(lca[1, 2] == 2)
diff --git a/spacy/tests/doc/test_span.py b/spacy/tests/doc/test_span.py
index 926624633..413bd0611 100644
--- a/spacy/tests/doc/test_span.py
+++ b/spacy/tests/doc/test_span.py
@@ -62,10 +62,24 @@ def test_spans_lca_matrix(en_tokenizer):
     tokens = en_tokenizer('the lazy dog slept')
     doc = get_doc(tokens.vocab, [t.text for t in tokens], heads=[2, 1, 1, 0])
     lca = doc[:2].get_lca_matrix()
-    assert(lca[0, 0] == 0)
-    assert(lca[0, 1] == -1)
-    assert(lca[1, 0] == -1)
-    assert(lca[1, 1] == 1)
+    assert lca.shape == (2, 2)
+    assert lca[0, 0] == 0  # the & the -> the
+    assert lca[0, 1] == -1 # the & lazy -> dog (out of span)
+    assert lca[1, 0] == -1 # lazy & the -> dog (out of span)
+    assert lca[1, 1] == 1  # lazy & lazy -> lazy
+
+    lca = doc[1:].get_lca_matrix()
+    assert lca.shape == (3, 3)
+    assert lca[0, 0] == 0 # lazy & lazy -> lazy
+    assert lca[0, 1] == 1 # lazy & dog -> dog
+    assert lca[0, 2] == 2 # lazy & slept -> slept
+
+    lca = doc[2:].get_lca_matrix()
+    assert lca.shape == (2, 2)
+    assert lca[0, 0] == 0 # dog & dog -> dog
+    assert lca[0, 1] == 1 # dog & slept -> slept
+    assert lca[1, 0] == 1 # slept & dog -> slept
+    assert lca[1, 1] == 1 # slept & slept -> slept
 
 
 def test_span_similarity_match():
diff --git a/spacy/tests/regression/test_issue2396.py b/spacy/tests/regression/test_issue2396.py
index c3ff04225..424c34ac1 100644
--- a/spacy/tests/regression/test_issue2396.py
+++ b/spacy/tests/regression/test_issue2396.py
@@ -6,9 +6,10 @@ from ..util import get_doc
 import pytest
 import numpy
 
-@pytest.mark.parametrize('sentence,matrix', [
+@pytest.mark.parametrize('sentence,heads,matrix', [
     (
         'She created a test for spacy',
+        [1, 0, 1, -2, -1, -1],
         numpy.array([
             [0, 1, 1, 1, 1, 1],
             [1, 1, 1, 1, 1, 1],
@@ -18,8 +19,9 @@ import numpy
             [1, 1, 3, 3, 4, 5]], dtype=numpy.int32)
     )
     ])
-def test_issue2396(EN, sentence, matrix):
-    doc = EN(sentence)
+def test_issue2396(en_tokenizer, sentence, heads, matrix):
+    tokens = en_tokenizer(sentence)
+    doc = get_doc(tokens.vocab, [t.text for t in tokens], heads=heads)
     span = doc[:]
     assert (doc.get_lca_matrix() == matrix).all()
     assert (span.get_lca_matrix() == matrix).all()
diff --git a/spacy/tokens/doc.pyx b/spacy/tokens/doc.pyx
index ae3b4fed6..ba39ac304 100644
--- a/spacy/tokens/doc.pyx
+++ b/spacy/tokens/doc.pyx
@@ -1,4 +1,3 @@
-
 # coding: utf8
 # cython: infer_types=True
 # cython: bounds_check=False
@@ -1051,21 +1050,30 @@ cdef int [:,:] _get_lca_matrix(Doc doc, int start, int end):
     cdef int [:,:] lca_matrix
 
     n_tokens= end - start
-    lca_matrix = numpy.empty((n_tokens, n_tokens), dtype=numpy.int32)
+    lca_mat = numpy.empty((n_tokens, n_tokens), dtype=numpy.int32)
+    lca_mat.fill(-1)
+    lca_matrix = lca_mat
 
-    for j in range(start, end):
-        token_j = doc[j]
+    for j in range(n_tokens):
+        token_j = doc[start + j]
         # the common ancestor of token and itself is itself:
         lca_matrix[j, j] = j
-        for k in range(j + 1, end):
-            lca = _get_tokens_lca(token_j, doc[k])
+        # we will only iterate through tokens in the same sentence
+        sent = token_j.sent
+        sent_start = sent.start
+        j_idx_in_sent = start + j - sent_start
+        n_missing_tokens_in_sent = len(sent) - j_idx_in_sent
+        # make sure we do not go past `end`, in cases where `end` < sent.end
+        max_range = min(j + n_missing_tokens_in_sent, end)
+        for k in range(j + 1, max_range):
+            lca = _get_tokens_lca(token_j, doc[start + k])
             # if lca is outside of span, we set it to -1
             if not start <= lca < end:
                 lca_matrix[j, k] = -1
                 lca_matrix[k, j] = -1
             else:
-                lca_matrix[j, k] = lca
-                lca_matrix[k, j] = lca
+                lca_matrix[j, k] = lca - start
+                lca_matrix[k, j] = lca - start
 
     return lca_matrix