diff --git a/Misc/NEWS b/Misc/NEWS
index 830a66a7e7e..0f19539a2a3 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -36,9 +36,9 @@ TO DO
 Core and Builtins
 -----------------
 
-- Int/Long unification is halfway complete.  There are a few broken tests,
-  the 'long' built-in hasn't been removed yet, and literals with trailing
-  'L' or 'l' are still recognized.  Performance may be sub-optimal.
+- Int/Long unification is halfway complete.  The 'long' built-in type
+  hasn't been removed yet, and literals with trailing 'L' or 'l' are
+  still recognized.  Performance may be sub-optimal.
 
 - 'except E, V' must now be spelled as 'except E as V' and deletes V
   at the end of the except clause; V must be a simple name.
diff --git a/Modules/_sqlite/statement.c b/Modules/_sqlite/statement.c
index 4e456361403..7763d10e4c3 100644
--- a/Modules/_sqlite/statement.c
+++ b/Modules/_sqlite/statement.c
@@ -100,7 +100,7 @@ int statement_bind_parameter(Statement* self, int pos, PyObject* parameter)
 
     if (parameter == Py_None) {
         rc = sqlite3_bind_null(self->st, pos);
-    } else if (PyInt_Check(parameter)) {
+    } else if (PyInt_CheckExact(parameter)) {
         longval = PyInt_AsLong(parameter);
         rc = sqlite3_bind_int64(self->st, pos, (sqlite_int64)longval);
 #ifdef HAVE_LONG_LONG
diff --git a/Objects/longobject.c b/Objects/longobject.c
index 03d22f5d8f6..250215ca8ba 100644
--- a/Objects/longobject.c
+++ b/Objects/longobject.c
@@ -364,7 +364,7 @@ PyLong_AsLong(PyObject *vv)
 		Py_DECREF(vv);
 	}
 	PyErr_SetString(PyExc_OverflowError,
-			"int too large to convert to int");
+			"Python int too large to convert to C long");
 	return -1;
 }
 
@@ -427,7 +427,7 @@ PyLong_AsSsize_t(PyObject *vv) {
 
  overflow:
 	PyErr_SetString(PyExc_OverflowError,
-			"int too large to convert to ");
+			"Python int too large to convert to C ssize_t");
 	return -1;
 }
 
@@ -462,7 +462,7 @@ PyLong_AsUnsignedLong(PyObject *vv)
 		x = (x << SHIFT) + v->ob_digit[i];
 		if ((x >> SHIFT) != prev) {
 			PyErr_SetString(PyExc_OverflowError,
-				"int too large to convert");
+			 "python int too large to convert to C unsigned long");
 			return (unsigned long) -1;
 		}
 	}
@@ -500,7 +500,7 @@ PyLong_AsSize_t(PyObject *vv)
 		x = (x << SHIFT) + v->ob_digit[i];
 		if ((x >> SHIFT) != prev) {
 			PyErr_SetString(PyExc_OverflowError,
-				"int too large to convert");
+			    "Python int too large to convert to C size_t");
 			return (unsigned long) -1;
 		}
 	}
@@ -943,7 +943,7 @@ PyLong_AsDouble(PyObject *vv)
 
 overflow:
 	PyErr_SetString(PyExc_OverflowError,
-		"int too large to convert to float");
+		"Python int too large to convert to C double");
 	return -1.0;
 }