diff --git a/spacy/syntax/arc_eager.pyx b/spacy/syntax/arc_eager.pyx
index 67e9fb2e7..cb0918606 100644
--- a/spacy/syntax/arc_eager.pyx
+++ b/spacy/syntax/arc_eager.pyx
@@ -69,7 +69,7 @@ cdef class ArcEager(TransitionSystem):
         for i in range(gold.length):
             if gold.heads[i] is None: # Missing values
                 gold.c_heads[i] = i
-                gold.c_labels[i] = self.strings['']
+                gold.c_labels[i] = -1
             else:
                 gold.c_heads[i] = gold.heads[i]
                 gold.c_labels[i] = self.strings[gold.labels[i]]
@@ -252,7 +252,9 @@ cdef int _right_cost(const Transition* self, const State* s, GoldParse gold) exc
     if gold.c_heads[s.i] == s.stack[0]:
         cost += self.label != gold.c_labels[s.i]
         return cost
-    cost += head_in_buffer(s, s.i, gold.c_heads)
+    # This indicates missing head
+    if gold.c_labels[s.i] != -1:
+        cost += head_in_buffer(s, s.i, gold.c_heads)
     cost += children_in_stack(s, s.i, gold.c_heads)
     cost += head_in_stack(s, s.i, gold.c_heads)
     if NON_MONOTONIC:
@@ -270,16 +272,18 @@ cdef int _left_cost(const Transition* self, const State* s, GoldParse gold) exce
     # If we're at EOL, then the left arc will add an arc to ROOT.
     elif at_eol(s):
         # Are we root?
-        cost += gold.c_heads[s.stack[0]] != s.stack[0]
-        # Are we labelling correctly?
-        cost += self.label != gold.c_labels[s.stack[0]]
+        if gold.c_labels[s.stack[0]] != -1:
+            cost += gold.c_heads[s.stack[0]] != s.stack[0]
+            # Are we labelling correctly?
+            cost += self.label != gold.c_labels[s.stack[0]]
         return cost
 
     cost += head_in_buffer(s, s.stack[0], gold.c_heads)
     cost += children_in_buffer(s, s.stack[0], gold.c_heads)
     if NON_MONOTONIC and s.stack_len >= 2:
         cost += gold.c_heads[s.stack[0]] == s.stack[-1]
-    cost += gold.c_heads[s.stack[0]] == s.stack[0]
+    if gold.c_labels[s.stack[0]] != -1:
+        cost += gold.c_heads[s.stack[0]] == s.stack[0]
     return cost