diff --git a/Makefile b/Makefile
index 5009aa9328984c..90e9744c6a2719 100644
--- a/Makefile
+++ b/Makefile
@@ -629,6 +629,7 @@ TEST_PROGRAMS_NEED_X += test-scrap-cache-tree
 TEST_PROGRAMS_NEED_X += test-sha1
 TEST_PROGRAMS_NEED_X += test-sha1-array
 TEST_PROGRAMS_NEED_X += test-sigchain
+TEST_PROGRAMS_NEED_X += test-strcmp-offset
 TEST_PROGRAMS_NEED_X += test-string-list
 TEST_PROGRAMS_NEED_X += test-submodule-config
 TEST_PROGRAMS_NEED_X += test-subprocess
diff --git a/cache.h b/cache.h
index 624cc4734d3cb6..15952c2c328365 100644
--- a/cache.h
+++ b/cache.h
@@ -591,6 +591,7 @@ extern int write_locked_index(struct index_state *, struct lock_file *lock, unsi
 extern int discard_index(struct index_state *);
 extern int unmerged_index(const struct index_state *);
 extern int verify_path(const char *path);
+extern int strcmp_offset(const char *s1_in, const char *s2_in, int *first_change);
 extern int index_dir_exists(struct index_state *istate, const char *name, int namelen);
 extern void adjust_dirname_case(struct index_state *istate, char *name);
 extern struct cache_entry *index_file_exists(struct index_state *istate, const char *name, int namelen, int igncase);
diff --git a/read-cache.c b/read-cache.c
index 01e3aa18313e12..e5070c60029a87 100644
--- a/read-cache.c
+++ b/read-cache.c
@@ -893,6 +893,34 @@ static int has_file_name(struct index_state *istate,
 	return retval;
 }
 
+/*
+ * Like strcmp(), but also return the offset of the first change.
+ */
+int strcmp_offset(const char *s1_in, const char *s2_in, int *first_change)
+{
+	const unsigned char *s1 = (const unsigned char *)s1_in;
+	const unsigned char *s2 = (const unsigned char *)s2_in;
+	int diff = 0;
+	int k;
+
+	*first_change = 0;
+	for (k=0; s1[k]; k++)
+		if ((diff = (s1[k] - s2[k])))
+			goto found_it;
+	if (!s2[k])
+		return 0;
+	diff = -1;
+
+found_it:
+	*first_change = k;
+	if (diff > 0)
+		return 1;
+	else if (diff < 0)
+		return -1;
+	else
+		return 0;
+}
+
 /*
  * Do we have another file with a pathname that is a proper
  * subset of the name we're trying to add?
@@ -904,6 +932,21 @@ static int has_dir_name(struct index_state *istate,
 	int stage = ce_stage(ce);
 	const char *name = ce->name;
 	const char *slash = name + ce_namelen(ce);
+	int len_eq_last;
+	int cmp_last = 0;
+
+	if (istate->cache_nr > 0) {
+		/*
+		 * Compare the entry's full path with the last path in the index.
+		 * If it sorts AFTER the last entry in the index and they have no
+		 * common prefix, then there cannot be any F/D name conflicts.
+		 */
+		cmp_last = strcmp_offset(name,
+			istate->cache[istate->cache_nr-1]->name,
+			&len_eq_last);
+		if (cmp_last > 0 && len_eq_last == 0)
+			return retval;
+	}
 
 	for (;;) {
 		int len;
@@ -916,6 +959,24 @@ static int has_dir_name(struct index_state *istate,
 		}
 		len = slash - name;
 
+		if (cmp_last > 0) {
+			/*
+			 * If this part of the directory prefix (including the trailing
+			 * slash) already appears in the path of the last entry in the
+			 * index, then we cannot also have a file with this prefix (or
+			 * any parent directory prefix).
+			 */
+			if (len+1 <= len_eq_last)
+				return retval;
+			/*
+			 * If this part of the directory prefix (excluding the trailing
+			 * slash) is longer than the known equal portions, then this part
+			 * of the prefix cannot collide with a file.  Go on to the parent.
+			 */
+			if (len > len_eq_last)
+				continue;
+		}
+
 		pos = index_name_stage_pos(istate, name, len, stage);
 		if (pos >= 0) {
 			/*
@@ -1007,7 +1068,16 @@ static int add_index_entry_with_check(struct index_state *istate, struct cache_e
 
 	if (!(option & ADD_CACHE_KEEP_CACHE_TREE))
 		cache_tree_invalidate_path(istate, ce->name);
-	pos = index_name_stage_pos(istate, ce->name, ce_namelen(ce), ce_stage(ce));
+
+	/*
+	 * If this entry's path sorts after the last entry in the index,
+	 * we can avoid searching for it.
+	 */
+	if (istate->cache_nr > 0 &&
+		strcmp(ce->name, istate->cache[istate->cache_nr - 1]->name) > 0)
+		pos = -istate->cache_nr - 1;
+	else
+		pos = index_name_stage_pos(istate, ce->name, ce_namelen(ce), ce_stage(ce));
 
 	/* existing match? Just replace it. */
 	if (pos >= 0) {
diff --git a/t/helper/.gitignore b/t/helper/.gitignore
index d6e8b3679872ab..0a89531a8b7f85 100644
--- a/t/helper/.gitignore
+++ b/t/helper/.gitignore
@@ -25,6 +25,7 @@
 /test-sha1
 /test-sha1-array
 /test-sigchain
+/test-strcmp-offset
 /test-string-list
 /test-submodule-config
 /test-subprocess
diff --git a/t/helper/test-strcmp-offset.c b/t/helper/test-strcmp-offset.c
new file mode 100644
index 00000000000000..56fd8c1e41b5eb
--- /dev/null
+++ b/t/helper/test-strcmp-offset.c
@@ -0,0 +1,59 @@
+#include "cache.h"
+
+struct test_data {
+	const char *s1;
+	const char *s2;
+	int first_change;
+};
+
+static struct test_data data[] = {
+	{ "abc", "abc", 0 },
+	{ "abc", "def", 0 },
+
+	{ "abc", "abz", 2 },
+
+	{ "abc", "abcdef", 3 },
+
+	{ "abc\xF0zzz", "abc\xFFzzz", 3 },
+
+	{ NULL, NULL, 0 }
+};
+
+int try_pair(const char *sa, const char *sb, int first_change)
+{
+	int failed = 0;
+	int offset, r_exp, r_tst;
+
+	r_exp = strcmp(sa, sb);
+	r_tst = strcmp_offset(sa, sb, &offset);
+	if (r_tst != r_exp) {
+		if ((r_tst < 0 && r_exp < 0) || (r_tst > 0 && r_exp > 0))
+			warning("'%s' vs '%s', imprecise result: %d != %d",
+				sa, sb, r_exp, r_tst);
+		else {
+			error("'%s' vs '%s', result expect %d, observed %d",
+			      sa, sb, r_exp, r_tst);
+			failed = 1;
+		}
+	}
+	if (offset != first_change) {
+		error("'%s' vs '%s', offset expect %d, observed %d",
+		      sa, sb, first_change, offset);
+		failed = 1;
+	}
+
+	return failed;
+}
+
+int cmd_main(int argc, const char **argv)
+{
+	int failed = 0;
+	int k;
+
+	for (k=0; data[k].s1; k++) {
+		failed += try_pair(data[k].s1, data[k].s2, data[k].first_change);
+		failed += try_pair(data[k].s2, data[k].s1, data[k].first_change);
+	}
+
+	return failed;
+}
diff --git a/t/t0065-strcmp-offset.sh b/t/t0065-strcmp-offset.sh
new file mode 100755
index 00000000000000..0176c8c9243e09
--- /dev/null
+++ b/t/t0065-strcmp-offset.sh
@@ -0,0 +1,11 @@
+#!/bin/sh
+
+test_description='Test strcmp_offset functionality'
+
+. ./test-lib.sh
+
+test_expect_success run_helper '
+	test-strcmp-offset
+'
+
+test_done