diff --git a/src/ZODB/Connection.py b/src/ZODB/Connection.py
index c067aa1e9..255f8438a 100644
--- a/src/ZODB/Connection.py
+++ b/src/ZODB/Connection.py
@@ -53,7 +53,6 @@
 from ZODB.serialize import ObjectWriter
 from ZODB.utils import oid_repr
 from ZODB.utils import p64
-from ZODB.utils import positive_id
 from ZODB.utils import u64
 from ZODB.utils import z64
 
@@ -947,15 +946,6 @@ def _release_resources(self):
             c._cache = PickleCache(self, 0, 0)
             c.close(False)
 
-    ##########################################################################
-    # Python protocol
-
-    def __repr__(self):
-        return '<Connection at %08x>' % (positive_id(self),)
-
-    # Python protocol
-    ##########################################################################
-
     ##########################################################################
     # DEPRECATION candidates
 
diff --git a/src/ZODB/cross-database-references.rst b/src/ZODB/cross-database-references.rst
index 6690d45b0..b5e043bc8 100644
--- a/src/ZODB/cross-database-references.rst
+++ b/src/ZODB/cross-database-references.rst
@@ -63,7 +63,7 @@ It isn't valid to create references outside a multi database:
     ...
     InvalidObjectReference:
       ('Attempt to store an object from a foreign database connection',
-       <Connection at ...>,
+       <ZODB.Connection.Connection object at ...>,
        <ZODB.tests.testcrossdatabasereferences.MyClass...>)
 
     >>> tm.abort()
@@ -92,7 +92,7 @@ reachable from multiple databases:
     InvalidObjectReference:
     ("A new object is reachable from multiple databases. Won't try to
     guess which one was correct!",
-    <Connection at ...>,
+    <ZODB.Connection.Connection object at ...>,
     <ZODB.tests.testcrossdatabasereferences.MyClass...>)
 
     >>> tm.abort()
@@ -120,7 +120,7 @@ This doesn't work with a savepoint:
     InvalidObjectReference:
     ("A new object is reachable from multiple databases. Won't try to guess
     which one was correct!",
-    <Connection at ...>,
+    <ZODB.Connection.Connection object at ...>,
     <ZODB.tests.testcrossdatabasereferences.MyClass...>)
 
     >>> tm.abort()
@@ -167,7 +167,7 @@ the other way around.
     ...
     InvalidObjectReference:
     ("Database '2' doesn't allow implicit cross-database references",
-    <Connection at ...>,
+    <ZODB.Connection.Connection object at ...>,
     {'x': {}})
 
     >>> transaction.abort()
diff --git a/src/ZODB/tests/multidb.txt b/src/ZODB/tests/multidb.txt
index e8dffcfec..78fea006f 100644
--- a/src/ZODB/tests/multidb.txt
+++ b/src/ZODB/tests/multidb.txt
@@ -86,12 +86,12 @@ You can (still) get a connection to a database this way:
     >>> tm = transaction.TransactionManager()
     >>> cn = db.open(transaction_manager=tm)
     >>> cn                  # doctest: +ELLIPSIS
-    <Connection at ...>
+    <ZODB.Connection.Connection object at ...>
 
 This is the only connection in this collection right now:
 
     >>> cn.connections      # doctest: +ELLIPSIS
-    {'root': <Connection at ...>}
+    {'root': <ZODB.Connection.Connection object at ...>}
 
 Getting a connection to a different database from an existing connection in the
 same database collection (this enables 'connection binding' within a given
@@ -99,7 +99,7 @@ thread/transaction/context ...):
 
     >>> cn2 = cn.get_connection('notroot')
     >>> cn2                  # doctest: +ELLIPSIS
-    <Connection at ...>
+    <ZODB.Connection.Connection object at ...>
 
 The second connection gets the same transaction manager as the first:
 
diff --git a/src/ZODB/tests/testcrossdatabasereferences.py b/src/ZODB/tests/testcrossdatabasereferences.py
index 3f1bbde6b..c6b96176e 100644
--- a/src/ZODB/tests/testcrossdatabasereferences.py
+++ b/src/ZODB/tests/testcrossdatabasereferences.py
@@ -61,7 +61,7 @@ def test_must_use_consistent_connections():
     InvalidObjectReference:
     ('Attempt to store a reference to an object from a separate connection to
     the same database or multidatabase',
-    <Connection at ...>,
+    <ZODB.Connection.Connection object at ...>,
     <ZODB.tests.testcrossdatabasereferences.MyClass object at ...>)
 
     >>> tm.abort()
@@ -80,7 +80,7 @@ def test_must_use_consistent_connections():
     InvalidObjectReference:
     ('Attempt to store a reference to an object from a separate connection
     to the same database or multidatabase',
-    <Connection at ...>,
+    <ZODB.Connection.Connection object at ...>,
     <ZODB.tests.testcrossdatabasereferences.MyClass object at ...>)
 
     >>> tm.abort()
diff --git a/src/ZODB/utils.py b/src/ZODB/utils.py
index 566b98f5a..ba46d0c11 100644
--- a/src/ZODB/utils.py
+++ b/src/ZODB/utils.py
@@ -41,7 +41,6 @@
            'oid_repr',
            'serial_repr',
            'tid_repr',
-           'positive_id',
            'readable_tid_repr',
            'get_pickle_metadata',
            'locked',
@@ -184,28 +183,6 @@ def readable_tid_repr(tid):
         result = "%s %s" % (result, TimeStamp(tid))
     return result
 
-# Addresses can "look negative" on some boxes, some of the time.  If you
-# feed a "negative address" to an %x format, Python 2.3 displays it as
-# unsigned, but produces a FutureWarning, because Python 2.4 will display
-# it as signed.  So when you want to prodce an address, use positive_id() to
-# obtain it.
-# _ADDRESS_MASK is 2**(number_of_bits_in_a_native_pointer).  Adding this to
-# a negative address gives a positive int with the same hex representation as
-# the significant bits in the original.
-
-
-_ADDRESS_MASK = 256 ** struct.calcsize('P')
-
-
-def positive_id(obj):
-    """Return id(obj) as a non-negative integer."""
-
-    result = id(obj)
-    if result < 0:
-        result += _ADDRESS_MASK
-        assert result > 0
-    return result
-
 # Given a ZODB pickle, return pair of strings (module_name, class_name).
 # Do this without importing the module or class object.
 # See ZODB/serialize.py's module docstring for the only docs that exist about