diff --git a/rdflib/plugins/serializers/trig.py b/rdflib/plugins/serializers/trig.py
index 479aae4d5..f8bd789d5 100644
--- a/rdflib/plugins/serializers/trig.py
+++ b/rdflib/plugins/serializers/trig.py
@@ -32,6 +32,7 @@ def __init__(self, store):
     def preprocess(self):
         for context in self.contexts:
             self.store = context
+            self.getQName(context.identifier)
             self._references = defaultdict(int)
             self._subjects = {}
 
@@ -40,22 +41,6 @@ def preprocess(self):
 
             self._contexts[context]=(self.orderSubjects(), self._subjects, self._references)
 
-
-    def preprocessTriple(self, triple):
-        s, p, o = triple
-        self._references[o]+=1
-        self._subjects[s] = True
-        for i, node in enumerate(triple):
-            if node in self.keywords:
-                continue
-            # Don't use generated prefixes for subjects and objects
-            self.getQName(node, gen_prefix=(i == VERB))
-            if isinstance(node, Literal) and node.datatype:
-                self.getQName(node.datatype, gen_prefix=_GEN_QNAME_FOR_DT)
-        p = triple[1]
-        if isinstance(p, BNode):
-            self._references[p]+=1
-
     def reset(self):
         super(TrigSerializer, self).reset()
         self._contexts = {}
@@ -83,7 +68,13 @@ def serialize(self, stream, base=None, encoding=None,
             if self.default_context and store.identifier==self.default_context:
                 self.write(self.indent() + '\n{')
             else:
-                self.write(self.indent() + '\n<%s> {' % self.getQName(store.identifier))
+                if isinstance(store.identifier, BNode):
+                    iri = store.identifier.n3()
+                else:
+                    iri = self.getQName(store.identifier)
+                    if iri is None:
+                        iri = store.identifier.n3()
+                self.write(self.indent() + '\n%s {' % iri)
 
             self.depth += 1
             for subject in ordered_subjects:
diff --git a/run_tests_py3.sh b/run_tests_py3.sh
index 30fc770e2..aa681ef92 100755
--- a/run_tests_py3.sh
+++ b/run_tests_py3.sh
@@ -16,4 +16,4 @@ cd build/py3_testing
 2to3 -wn --no-diffs test
 2to3 -wn --no-diffs run_tests.py
 
-python3 run_tests.py
+python3 run_tests.py $@
diff --git a/test/test_trig.py b/test/test_trig.py
index abcbe1b97..e05f483ef 100644
--- a/test/test_trig.py
+++ b/test/test_trig.py
@@ -4,6 +4,10 @@
 
 from rdflib.py3compat import b
 
+TRIPLE = (rdflib.URIRef("http://example.com/s"),
+          rdflib.RDFS.label,
+          rdflib.Literal("example 1"))
+
 class TestTrig(unittest.TestCase):
 
     def testEmpty(self):
@@ -46,3 +50,35 @@ def testSameSubject(self):
         self.assertEqual(len(re.findall(b("p2"), s)), 1)
 
         self.assert_(b('{}') not in s) # no empty graphs!
+
+    def testRememberNamespace(self):
+        g = rdflib.ConjunctiveGraph()
+        g.add(TRIPLE + (rdflib.URIRef("http://example.com/graph1"),))
+        # In 4.2.0 the first serialization would fail to include the
+        # prefix for the graph but later serialize() calls would work.
+        first_out = g.serialize(format='trig')
+        second_out = g.serialize(format='trig')
+        self.assert_(b'@prefix ns1: <http://example.com/> .' in second_out)
+        self.assert_(b'@prefix ns1: <http://example.com/> .' in first_out)
+
+    def testGraphQnameSyntax(self):
+        g = rdflib.ConjunctiveGraph()
+        g.add(TRIPLE + (rdflib.URIRef("http://example.com/graph1"),))
+        out = g.serialize(format='trig')
+        self.assert_(b'ns1:graph1 {' in out)
+
+    def testGraphUriSyntax(self):
+        g = rdflib.ConjunctiveGraph()
+        # getQName will not abbreviate this, so it should serialize as
+        # a '<...>' term.
+        g.add(TRIPLE + (rdflib.URIRef("http://example.com/foo."),))
+        out = g.serialize(format='trig')
+        self.assert_(b'<http://example.com/foo.> {' in out)
+
+    def testBlankGraphIdentifier(self):
+        g = rdflib.ConjunctiveGraph()
+        g.add(TRIPLE + (rdflib.BNode(),))
+        out = g.serialize(format='trig')
+        graph_label_line = out.splitlines()[-4]
+        self.assert_(re.match(br'^_:[a-zA-Z0-9]+ \{', graph_label_line))
+