diff --git a/Objects/fileobject.c b/Objects/fileobject.c
index edd839e..737ebb7 100644
--- a/Objects/fileobject.c
+++ b/Objects/fileobject.c
@@ -992,12 +992,6 @@
 #define SMALLCHUNK BUFSIZ
 #endif
 
-#if SIZEOF_INT < 4
-#define BIGCHUNK  (512 * 32)
-#else
-#define BIGCHUNK  (512 * 1024)
-#endif
-
 static size_t
 new_buffersize(PyFileObject *f, size_t currentsize)
 {
@@ -1026,15 +1020,10 @@
         /* Add 1 so if the file were to grow we'd notice. */
     }
 #endif
-    if (currentsize > SMALLCHUNK) {
-        /* Keep doubling until we reach BIGCHUNK;
-           then keep adding BIGCHUNK. */
-        if (currentsize <= BIGCHUNK)
-            return currentsize + currentsize;
-        else
-            return currentsize + BIGCHUNK;
-    }
-    return currentsize + SMALLCHUNK;
+    /* Expand the buffer by an amount proportional to the current size,
+       giving us amortized linear-time behavior. Use a less-than-double
+       growth factor to avoid excessive allocation. */
+    return currentsize + (currentsize >> 3) + 6;
 }
 
 #if defined(EWOULDBLOCK) && defined(EAGAIN) && EWOULDBLOCK != EAGAIN