diff --git a/python/CHANGELOG.rst b/python/CHANGELOG.rst
index f1b1ce75ee..809c96c002 100644
--- a/python/CHANGELOG.rst
+++ b/python/CHANGELOG.rst
@@ -19,11 +19,18 @@ In development
   children on an interval. Previously an error was thrown when some operation
   building the trees was attempted. (:user:`jeromekelleher`, :pr:`709`).
 
+- The TableCollection object no longer implements the iterator protocol.
+  Previously ``list(tables)`` returned a sequence of (table_name, table_instance)
+  tuples. This has been replaced with the more intuitive and future-proof
+  TableCollection.name_map and TreeSequence.tables_dict attributes, which
+  perform the same function. (:user:`jeromekelleher`, :issue:`500`,
+  :pr:`694`)
+
 **New features**
 
 - New methods to perform set operations on TableCollections and TreeSequences.
   ``TableCollection.subset`` subsets and reorders table collections by nodes
-  (:user:`mufernando`, :user:`petrelharp`, :pr:`663`, :pr:`690`). 
+  (:user:`mufernando`, :user:`petrelharp`, :pr:`663`, :pr:`690`).
   ``TableCollection.union`` forms the node-wise union of two table collections
   (:user:`mufernando`, :user:`petrelharp`, :issue:`381` :pr:`623`).
 
diff --git a/python/tests/test_highlevel.py b/python/tests/test_highlevel.py
index 84ce5421d6..92f45154ad 100644
--- a/python/tests/test_highlevel.py
+++ b/python/tests/test_highlevel.py
@@ -1328,7 +1328,7 @@ def test_at(self):
 
     def test_sequence_iteration(self):
         for ts in get_example_tree_sequences():
-            for table_name, _ in ts.tables:
+            for table_name in ts.tables_dict.keys():
                 sequence = getattr(ts, table_name)()
                 length = getattr(ts, "num_" + table_name)
                 # Test __iter__
diff --git a/python/tests/test_tables.py b/python/tests/test_tables.py
index 9ae67e386a..992b63b3ac 100644
--- a/python/tests/test_tables.py
+++ b/python/tests/test_tables.py
@@ -25,7 +25,6 @@
 between simulations and the tree sequence.
 """
 import io
-import itertools
 import json
 import math
 import pickle
@@ -1590,15 +1589,11 @@ class TestTablesToTreeSequence(unittest.TestCase):
     Tests for the .tree_sequence() method of a TableCollection.
     """
 
-    random_seed = 42
-
     def test_round_trip(self):
-        a = msprime.simulate(5, mutation_rate=1, random_seed=self.random_seed)
+        a = msprime.simulate(5, mutation_rate=1, random_seed=42)
         tables = a.dump_tables()
         b = tables.tree_sequence()
-        self.assertTrue(
-            all(a == b for a, b in zip(a.tables, b.tables) if a[0] != "provenances")
-        )
+        self.assertEqual(a.tables, b.tables)
 
 
 class TestMutationTimeErrors(unittest.TestCase):
@@ -2040,19 +2035,25 @@ def test_roundtrip_dict(self):
         t2 = tskit.TableCollection.fromdict(t1.asdict())
         self.assertEqual(t1, t2)
 
-    def test_iter(self):
-        def test_iter(table_collection):
-            table_names = [
-                attr_name
-                for attr_name in sorted(dir(table_collection))
-                if isinstance(getattr(table_collection, attr_name), tskit.BaseTable)
-            ]
-            for n in table_names:
-                yield n, getattr(table_collection, n)
-
+    def test_name_map(self):
         ts = msprime.simulate(10, mutation_rate=1, random_seed=1)
-        for t1, t2 in itertools.zip_longest(test_iter(ts.tables), ts.tables):
-            self.assertEquals(t1, t2)
+        tables = ts.tables
+        td1 = {
+            "individuals": tables.individuals,
+            "populations": tables.populations,
+            "nodes": tables.nodes,
+            "edges": tables.edges,
+            "sites": tables.sites,
+            "mutations": tables.mutations,
+            "migrations": tables.migrations,
+            "provenances": tables.provenances,
+        }
+        td2 = tables.name_map
+        self.assertIsInstance(td2, dict)
+        self.assertEqual(set(td1.keys()), set(td2.keys()))
+        for name in td2.keys():
+            self.assertEqual(td1[name], td2[name])
+        self.assertEqual(td1, td2)
 
     def test_equals_empty(self):
         self.assertEqual(tskit.TableCollection(), tskit.TableCollection())
diff --git a/python/tests/test_topology.py b/python/tests/test_topology.py
index 6424fc6a94..39be7b800a 100644
--- a/python/tests/test_topology.py
+++ b/python/tests/test_topology.py
@@ -53,8 +53,12 @@ def tables_equal(table_collection_1, table_collection_2, compare_provenances=Tru
     """
     Check equality of tables, ignoring provenance timestamps (but not contents)
     """
-    for (_, table_1), (_, table_2) in zip(table_collection_1, table_collection_2):
-        if isinstance(table_1, tskit.ProvenanceTable):
+    tc_dict_1 = table_collection_1.name_map
+    tc_dict_2 = table_collection_2.name_map
+    for table_name in tc_dict_1.keys():
+        table_1 = tc_dict_1[table_name]
+        table_2 = tc_dict_2[table_name]
+        if table_name == "provenances":
             if compare_provenances:
                 if np.any(table_1.record != table_2.record):
                     return False
diff --git a/python/tskit/tables.py b/python/tskit/tables.py
index 00b6b22d5a..54b317d2d5 100644
--- a/python/tskit/tables.py
+++ b/python/tskit/tables.py
@@ -1966,7 +1966,7 @@ def asdict(self):
         """
         Returns a dictionary representation of this TableCollection.
 
-        Note: the semantics of this method changed at tskit 1.0.0. Previously a
+        Note: the semantics of this method changed at tskit 0.1.0. Previously a
         map of table names to the tables themselves was returned.
         """
         return {
@@ -1984,6 +1984,24 @@ def asdict(self):
             "provenances": self.provenances.asdict(),
         }
 
+    @property
+    def name_map(self):
+        """
+        Returns a dictionary mapping table names to the corresponding
+        table instances. For example, the returned dictionary will contain the
+        key "edges" that maps to an :class:`.EdgeTable` instance.
+        """
+        return {
+            "edges": self.edges,
+            "individuals": self.individuals,
+            "migrations": self.migrations,
+            "mutations": self.mutations,
+            "nodes": self.nodes,
+            "populations": self.populations,
+            "provenances": self.provenances,
+            "sites": self.sites,
+        }
+
     def __banner(self, title):
         width = 60
         line = "#" * width
@@ -1992,20 +2010,6 @@ def __banner(self, title):
         title_line += "#"
         return line + "\n" + title_line + "\n" + line + "\n"
 
-    def __iter__(self):
-        """
-        Iterate over all the tables in this TableCollection, ordered by table name
-        (i.e. deterministically), returning a tuple of (table_name, table_object)
-        """
-        yield "edges", self.edges
-        yield "individuals", self.individuals
-        yield "migrations", self.migrations
-        yield "mutations", self.mutations
-        yield "nodes", self.nodes
-        yield "populations", self.populations
-        yield "provenances", self.provenances
-        yield "sites", self.sites
-
     def __str__(self):
         s = self.__banner("Individuals")
         s += str(self.individuals) + "\n"
diff --git a/python/tskit/trees.py b/python/tskit/trees.py
index e0a0617f87..c9efeb9696 100644
--- a/python/tskit/trees.py
+++ b/python/tskit/trees.py
@@ -2940,6 +2940,15 @@ def dump(self, path, zlib_compression=False):
         # Convert the path to str to allow us use Pathlib inputs
         self._ll_tree_sequence.dump(str(path))
 
+    @property
+    def tables_dict(self):
+        """
+        Returns a dictionary mapping names to tables in the
+        underlying :class:`.TableCollection`. Equivalent to calling
+        ``ts.tables.name_map``.
+        """
+        return self.tables.name_map
+
     @property
     def tables(self):
         """