diff --git a/src/grep.c b/src/grep.c
index 9c933e4..4109ae4 100644
--- a/src/grep.c
+++ b/src/grep.c
@@ -984,7 +984,7 @@ fillbuf (idx_t save, struct stat const *st)
               ptrdiff_t a;
               if (0 <= to_be_read
                   && INT_ADD_OK (to_be_read, save + min_after_buflim, &a))
-                alloc_max = a;
+                alloc_max = MAX (a, bufalloc + incr_min);
             }
 
           newbuf = xpalloc (NULL, &bufalloc, incr_min, alloc_max, 1);
diff --git a/tests/Makefile.am b/tests/Makefile.am
index 04a9eee..708980d 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -104,6 +104,7 @@ TESTS =						\
   fgrep-longest					\
   file						\
   filename-lineno.pl				\
+  fillbuf-long-line				\
   fmbtest					\
   foad1						\
   grep-dev-null					\
diff --git a/tests/fillbuf-long-line b/tests/fillbuf-long-line
new file mode 100755
index 0000000..5a8d339
--- /dev/null
+++ b/tests/fillbuf-long-line
@@ -0,0 +1,11 @@
+#!/bin/sh
+# This would fail for v3.7-15-ge3694e9 .. grep-v3.7-48-g5c3c427
+. "${srcdir=.}/init.sh"; path_prepend_ ../src
+
+printf %0104681d 0 > in || framework_failure_
+
+fail=0
+
+returns_ 1 grep xx in || fail=1
+
+Exit $fail