diff --git a/Lib/test/test_memoryio.py b/Lib/test/test_memoryio.py
index 0b5ec9f..d538a7e 100644
--- a/Lib/test/test_memoryio.py
+++ b/Lib/test/test_memoryio.py
@@ -80,6 +80,9 @@
         self.assertEqual(memio.getvalue(), buf[:6])
         self.assertEqual(memio.truncate(4), 4)
         self.assertEqual(memio.getvalue(), buf[:4])
+        # truncate() accepts long objects
+        self.assertEqual(memio.truncate(4L), 4)
+        self.assertEqual(memio.getvalue(), buf[:4])
         self.assertEqual(memio.tell(), 4)
         memio.write(buf)
         self.assertEqual(memio.getvalue(), buf[:4] + buf)
@@ -107,7 +110,8 @@
 
         self.assertEqual(memio.read(0), self.EOF)
         self.assertEqual(memio.read(1), buf[:1])
-        self.assertEqual(memio.read(4), buf[1:5])
+        # read() accepts long objects
+        self.assertEqual(memio.read(4L), buf[1:5])
         self.assertEqual(memio.read(900), buf[5:])
         self.assertEqual(memio.read(), self.EOF)
         memio.seek(0)
@@ -136,7 +140,8 @@
         self.assertEqual(memio.readline(), self.EOF)
         memio.seek(0)
         self.assertEqual(memio.readline(5), buf[:5])
-        self.assertEqual(memio.readline(5), buf[5:10])
+        # readline() accepts long objects
+        self.assertEqual(memio.readline(5L), buf[5:10])
         self.assertEqual(memio.readline(5), buf[10:15])
         memio.seek(0)
         self.assertEqual(memio.readline(-1), buf)
@@ -164,7 +169,8 @@
         memio.seek(5)
         self.assertEqual(memio.readlines(), [buf[5:]] + [buf] * 9)
         memio.seek(0)
-        self.assertEqual(memio.readlines(15), [buf] * 2)
+        # readlines() accepts long objects
+        self.assertEqual(memio.readlines(15L), [buf] * 2)
         memio.seek(0)
         self.assertEqual(memio.readlines(-1), [buf] * 10)
         memio.seek(0)
@@ -225,6 +231,8 @@
         self.assertEqual(memio.seek(0, 0), 0)
         self.assertEqual(memio.read(), buf)
         self.assertEqual(memio.seek(3), 3)
+        # seek() accepts long objects
+        self.assertEqual(memio.seek(3L), 3)
         self.assertEqual(memio.seek(0, 1), 3)
         self.assertEqual(memio.read(), buf[3:])
         self.assertEqual(memio.seek(len(buf)), len(buf))
diff --git a/Misc/NEWS b/Misc/NEWS
index 23a0e4c..7bcad72 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -24,6 +24,9 @@
 Library
 -------
 
+- Issue #7249: Methods of io.BytesIO now allow `long` as well as `int`
+  arguments.
+
 - Issue #6665: Fix fnmatch to properly match filenames with newlines in them.
 
 - Issue #1008086: Fixed socket.inet_aton() to always return 4 bytes even on
diff --git a/Modules/_bytesio.c b/Modules/_bytesio.c
index c5c14b3..d342838 100644
--- a/Modules/_bytesio.c
+++ b/Modules/_bytesio.c
@@ -219,8 +219,8 @@
     if (!PyArg_ParseTuple(args, "|O:read", &arg))
         return NULL;
 
-    if (PyInt_Check(arg)) {
-        size = PyInt_AsSsize_t(arg);
+    if (PyIndex_Check(arg)) {
+        size = PyNumber_AsSsize_t(arg, PyExc_OverflowError);
         if (size == -1 && PyErr_Occurred())
             return NULL;
     }
@@ -288,8 +288,8 @@
     if (!PyArg_ParseTuple(args, "|O:readline", &arg))
         return NULL;
 
-    if (PyInt_Check(arg)) {
-        size = PyInt_AsSsize_t(arg);
+    if (PyIndex_Check(arg)) {
+        size = PyNumber_AsSsize_t(arg, PyExc_OverflowError);
         if (size == -1 && PyErr_Occurred())
             return NULL;
     }
@@ -334,8 +334,8 @@
     if (!PyArg_ParseTuple(args, "|O:readlines", &arg))
         return NULL;
 
-    if (PyInt_Check(arg)) {
-        maxsize = PyInt_AsSsize_t(arg);
+    if (PyIndex_Check(arg)) {
+        maxsize = PyNumber_AsSsize_t(arg, PyExc_OverflowError);
         if (maxsize == -1 && PyErr_Occurred())
             return NULL;
     }
@@ -419,8 +419,8 @@
     if (!PyArg_ParseTuple(args, "|O:truncate", &arg))
         return NULL;
 
-    if (PyInt_Check(arg)) {
-        size = PyInt_AsSsize_t(arg);
+    if (PyIndex_Check(arg)) {
+        size = PyNumber_AsSsize_t(arg, PyExc_OverflowError);
         if (size == -1 && PyErr_Occurred())
             return NULL;
     }