diff --git a/OpenSSL/SSL.py b/OpenSSL/SSL.py
index 48c8227..1e85795 100644
--- a/OpenSSL/SSL.py
+++ b/OpenSSL/SSL.py
@@ -1,17 +1,17 @@
 
-from functools import wraps
+from functools import wraps, partial
 from itertools import count
 from weakref import WeakValueDictionary
 from errno import errorcode
 
-from cryptography.hazmat.backends.openssl import backend
-_ffi = backend.ffi
-_lib = backend.lib
+from OpenSSL._util import (
+    ffi as _ffi,
+    lib as _lib,
+    new_mem_buf as _new_mem_buf,
+    exception_from_error_queue as _exception_from_error_queue)
 
 from OpenSSL.crypto import (
-    FILETYPE_PEM, _PassphraseHelper, PKey, X509Name, X509, X509Store,
-
-    _raise_current_error, _new_mem_buf)
+    FILETYPE_PEM, _PassphraseHelper, PKey, X509Name, X509, X509Store)
 
 _unspecified = object()
 
@@ -104,6 +104,39 @@
 SSL_CB_HANDSHAKE_DONE = _lib.SSL_CB_HANDSHAKE_DONE
 
 
+class Error(Exception):
+    pass
+
+
+
+_raise_current_error = partial(_exception_from_error_queue, Error)
+
+
+class WantReadError(Error):
+    pass
+
+
+
+class WantWriteError(Error):
+    pass
+
+
+
+class WantX509LookupError(Error):
+    pass
+
+
+
+class ZeroReturnError(Error):
+    pass
+
+
+
+class SysCallError(Error):
+    pass
+
+
+
 class _VerifyHelper(object):
     def __init__(self, connection, callback):
         self._problems = []
@@ -134,41 +167,13 @@
     def raise_if_problem(self):
         if self._problems:
             try:
-                _raise_current_error(Error)
+                _raise_current_error()
             except Error:
                 pass
             raise self._problems.pop(0)
 
 
 
-class Error(Exception):
-    pass
-
-
-
-class WantReadError(Error):
-    pass
-
-
-
-class WantWriteError(Error):
-    pass
-
-
-
-class WantX509LookupError(Error):
-    pass
-
-
-
-class ZeroReturnError(Error):
-    pass
-
-
-class SysCallError(Error):
-    pass
-
-
 def _asFileDescriptor(obj):
     fd = None
 
@@ -284,7 +289,7 @@
 
         load_result = _lib.SSL_CTX_load_verify_locations(self._context, cafile, capath)
         if not load_result:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def _wrap_callback(self, callback):
@@ -323,7 +328,7 @@
         set_result = _lib.SSL_CTX_set_default_verify_paths(self._context)
         if not set_result:
             1/0
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def use_certificate_chain_file(self, certfile):
@@ -338,7 +343,7 @@
 
         result = _lib.SSL_CTX_use_certificate_chain_file(self._context, certfile)
         if not result:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def use_certificate_file(self, certfile, filetype=FILETYPE_PEM):
@@ -356,7 +361,7 @@
 
         use_result = _lib.SSL_CTX_use_certificate_file(self._context, certfile, filetype)
         if not use_result:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def use_certificate(self, cert):
@@ -371,7 +376,7 @@
 
         use_result = _lib.SSL_CTX_use_certificate(self._context, cert._x509)
         if not use_result:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def add_extra_chain_cert(self, certobj):
@@ -388,13 +393,13 @@
         add_result = _lib.SSL_CTX_add_extra_chain_cert(self._context, copy)
         if not add_result:
             # _lib.X509_free(copy)
-            # _raise_current_error(Error)
+            # _raise_current_error()
             1/0
 
 
     def _raise_passphrase_exception(self):
         if self._passphrase_helper is None:
-            _raise_current_error(Error)
+            _raise_current_error()
         exception = self._passphrase_helper.raise_if_problem(Error)
         if exception is not None:
             raise exception
@@ -550,7 +555,7 @@
 
         bio = _lib.BIO_new_file(dhfile, "r")
         if bio == _ffi.NULL:
-            _raise_current_error(Error)
+            _raise_current_error()
         bio = _ffi.gc(bio, _lib.BIO_free)
 
         dh = _lib.PEM_read_bio_DHparams(bio, _ffi.NULL, _ffi.NULL, _ffi.NULL)
@@ -570,7 +575,7 @@
 
         result = _lib.SSL_CTX_set_cipher_list(self._context, cipher_list)
         if not result:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def set_client_ca_list(self, certificate_authorities):
@@ -586,7 +591,7 @@
         name_stack = _lib.sk_X509_NAME_new_null()
         if name_stack == _ffi.NULL:
             1/0
-            _raise_current_error(Error)
+            _raise_current_error()
 
         try:
             for ca_name in certificate_authorities:
@@ -597,11 +602,11 @@
                 copy = _lib.X509_NAME_dup(ca_name._name)
                 if copy == _ffi.NULL:
                     1/0
-                    _raise_current_error(Error)
+                    _raise_current_error()
                 push_result = _lib.sk_X509_NAME_push(name_stack, copy)
                 if not push_result:
                     _lib.X509_NAME_free(copy)
-                    _raise_current_error(Error)
+                    _raise_current_error()
         except:
             _lib.sk_X509_NAME_free(name_stack)
             raise
@@ -626,7 +631,7 @@
             self._context, certificate_authority._x509)
         if not add_result:
             1/0
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def set_timeout(self, timeout):
@@ -822,11 +827,11 @@
             else:
                 # TODO Untested
                 1/0
-                _raise_current_error(Error)
+                _raise_current_error()
         elif error == _lib.SSL_ERROR_NONE:
             pass
         else:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def get_context(self):
@@ -979,7 +984,7 @@
         else:
             1/0
             # TODO Untested
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
     def bio_read(self, bufsiz):
@@ -1162,7 +1167,7 @@
             copy = _lib.X509_NAME_dup(name)
             if copy == _ffi.NULL:
                 1/0
-                _raise_current_error(Error)
+                _raise_current_error()
 
             pyname = X509Name.__new__(X509Name)
             pyname._name = _ffi.gc(copy, _lib.X509_NAME_free)
@@ -1379,6 +1384,6 @@
 
         result = _lib.SSL_set_session(self._ssl, session._session)
         if not result:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 ConnectionType = Connection
diff --git a/OpenSSL/_util.py b/OpenSSL/_util.py
new file mode 100644
index 0000000..4062fe5
--- /dev/null
+++ b/OpenSSL/_util.py
@@ -0,0 +1,35 @@
+from cryptography.hazmat.backends.openssl import backend
+ffi = backend.ffi
+lib = backend.lib
+
+def exception_from_error_queue(exceptionType):
+    errors = []
+    while True:
+        error = lib.ERR_get_error()
+        if error == 0:
+            break
+        errors.append((
+                ffi.string(lib.ERR_lib_error_string(error)),
+                ffi.string(lib.ERR_func_error_string(error)),
+                ffi.string(lib.ERR_reason_error_string(error))))
+
+    raise exceptionType(errors)
+
+
+
+def new_mem_buf(buffer=None):
+    if buffer is None:
+        bio = lib.BIO_new(lib.BIO_s_mem())
+        free = lib.BIO_free
+    else:
+        data = ffi.new("char[]", buffer)
+        bio = lib.BIO_new_mem_buf(data, len(buffer))
+        # Keep the memory alive as long as the bio is alive!
+        def free(bio, ref=data):
+            return lib.BIO_free(bio)
+
+    if bio == ffi.NULL:
+        1/0
+
+    bio = ffi.gc(bio, free)
+    return bio
diff --git a/OpenSSL/crypto.py b/OpenSSL/crypto.py
index 1a4db38..e699f37 100644
--- a/OpenSSL/crypto.py
+++ b/OpenSSL/crypto.py
@@ -1,8 +1,11 @@
 from time import time
+from functools import partial
 
-from cryptography.hazmat.backends.openssl import backend
-_ffi = backend.ffi
-_lib = backend.lib
+from OpenSSL._util import (
+    ffi as _ffi,
+    lib as _lib,
+    new_mem_buf as _new_mem_buf,
+    exception_from_error_queue as _exception_from_error_queue)
 
 FILETYPE_PEM = _lib.SSL_FILETYPE_PEM
 FILETYPE_ASN1 = _lib.SSL_FILETYPE_ASN1
@@ -14,6 +17,13 @@
 TYPE_DSA = _lib.EVP_PKEY_DSA
 
 
+class Error(Exception):
+    pass
+
+
+_raise_current_error = partial(_exception_from_error_queue, Error)
+
+
 def _bio_to_string(bio):
     """
     Copy the contents of an OpenSSL BIO object into a Python byte string.
@@ -24,25 +34,6 @@
 
 
 
-def _new_mem_buf(buffer=None):
-    if buffer is None:
-        bio = _lib.BIO_new(_lib.BIO_s_mem())
-        free = _lib.BIO_free
-    else:
-        data = _ffi.new("char[]", buffer)
-        bio = _lib.BIO_new_mem_buf(data, len(buffer))
-        # Keep the memory alive as long as the bio is alive!
-        def free(bio, ref=data):
-            return _lib.BIO_free(bio)
-
-    if bio == _ffi.NULL:
-        1/0
-
-    bio = _ffi.gc(bio, free)
-    return bio
-
-
-
 def _set_asn1_time(boundary, when):
     if not isinstance(when, bytes):
         raise TypeError("when must be a byte string")
@@ -83,28 +74,6 @@
 
 
 
-class Error(Exception):
-    pass
-
-
-
-def _raise_current_error(exceptionType=Error):
-    errors = []
-    while True:
-        error = _lib.ERR_get_error()
-        if error == 0:
-            break
-        errors.append((
-                _ffi.string(_lib.ERR_lib_error_string(error)),
-                _ffi.string(_lib.ERR_func_error_string(error)),
-                _ffi.string(_lib.ERR_reason_error_string(error))))
-
-    raise exceptionType(errors)
-
-_exception_from_error_queue = _raise_current_error
-
-
-
 class PKey(object):
     _only_public = False
     _initialized = True
@@ -660,7 +629,7 @@
 
         result = _lib.X509_REQ_verify(self._req, pkey._pkey)
         if result <= 0:
-            _raise_current_error(Error)
+            _raise_current_error()
 
         return result
 
@@ -1105,7 +1074,7 @@
 
         result = _lib.X509_STORE_add_cert(self._store, cert._x509)
         if not result:
-            _raise_current_error(Error)
+            _raise_current_error()
 
 
 X509StoreType = X509Store
@@ -1848,7 +1817,7 @@
 
     def raise_if_problem(self, exceptionType=Error):
         try:
-            _raise_current_error(exceptionType)
+            _exception_from_error_queue(exceptionType)
         except exceptionType as e:
             pass
         if self._problems:
diff --git a/OpenSSL/rand.py b/OpenSSL/rand.py
index 8295854..0204118 100644
--- a/OpenSSL/rand.py
+++ b/OpenSSL/rand.py
@@ -6,14 +6,18 @@
 
 import __builtin__
 
-from cryptography.hazmat.backends.openssl import backend
-_lib = backend.lib
-_ffi = backend.ffi
+from functools import partial
 
-# TODO Nothing tests the existence or use of this
+from OpenSSL._util import (
+    ffi as _ffi,
+    lib as _lib,
+    exception_from_error_queue as _exception_from_error_queue)
+
+
 class Error(Exception):
     pass
 
+_raise_current_error = partial(_exception_from_error_queue, Error)
 
 _unspecified = object()
 
@@ -33,7 +37,10 @@
     result_buffer = _ffi.new("char[]", num_bytes)
     result_code = _lib.RAND_bytes(result_buffer, num_bytes)
     if result_code == -1:
-        raise Exception("zoops") # TODO
+        # TODO: No tests for this code path.  Triggering a RAND_bytes failure
+        # might involve supplying a custom ENGINE?  That's hard.
+        _raise_current_error()
+
     return _ffi.buffer(result_buffer)[:]
 
 
diff --git a/OpenSSL/test/test_rand.py b/OpenSSL/test/test_rand.py
index 8a3c5fe..ffbb731 100644
--- a/OpenSSL/test/test_rand.py
+++ b/OpenSSL/test/test_rand.py
@@ -23,7 +23,14 @@
         self.assertRaises(TypeError, rand.bytes, None)
         self.assertRaises(TypeError, rand.bytes, 3, None)
 
-    # XXX Test failure of the malloc() in rand_bytes.
+
+    def test_insufficientMemory(self):
+        """
+        :py:obj:`OpenSSL.rand.bytes` raises :py:obj:`MemoryError` if more bytes
+        are requested than will fit in memory.
+        """
+        self.assertRaises(MemoryError, rand.bytes, 1024 * 1024 * 1024 * 1024)
+
 
     def test_bytes(self):
         """
diff --git a/OpenSSL/test/util.py b/OpenSSL/test/util.py
index 31242ce..a1a0cd9 100644
--- a/OpenSSL/test/util.py
+++ b/OpenSSL/test/util.py
@@ -14,7 +14,8 @@
 from unittest import TestCase
 import sys
 
-from OpenSSL.crypto import Error, _exception_from_error_queue
+from OpenSSL._util import exception_from_error_queue
+from OpenSSL.crypto import Error
 
 import memdbg
 
@@ -167,7 +168,7 @@
                 elif os.path.exists(temp):
                     os.unlink(temp)
         try:
-            _exception_from_error_queue()
+            exception_from_error_queue(Error)
         except Error:
             e = sys.exc_info()[1]
             if e.args != ([],):