diff --git a/t/t0060-path-utils.sh b/t/t0060-path-utils.sh
index 8336114f98..86000e26c1 100755
--- a/t/t0060-path-utils.sh
+++ b/t/t0060-path-utils.sh
@@ -7,41 +7,91 @@ test_description='Test various path utilities'
 
 . ./test-lib.sh
 
-norm_abs() {
-	test_expect_success "normalize absolute: $1 => $2" \
+norm_path() {
+	test_expect_success $3 "normalize path: $1 => $2" \
 	"test \"\$(test-path-utils normalize_path_copy '$1')\" = '$2'"
 }
 
+# On Windows, we are using MSYS's bash, which mangles the paths.
+# Absolute paths are anchored at the MSYS installation directory,
+# which means that the path / accounts for this many characters:
+rootoff=$(test-path-utils normalize_path_copy / | wc -c)
+# Account for the trailing LF:
+if test "$rootoff" = 2; then
+	rootoff=	# we are on Unix
+else
+	rootoff=$(($rootoff-1))
+fi
+
 ancestor() {
-	test_expect_success "longest ancestor: $1 $2 => $3" \
-	"test \"\$(test-path-utils longest_ancestor_length '$1' '$2')\" = '$3'"
+	# We do some math with the expected ancestor length.
+	expected=$3
+	if test -n "$rootoff" && test "x$expected" != x-1; then
+		expected=$(($expected+$rootoff))
+	fi
+	test_expect_success "longest ancestor: $1 $2 => $expected" \
+	"actual=\$(test-path-utils longest_ancestor_length '$1' '$2') &&
+	 test \"\$actual\" = '$expected'"
 }
 
-norm_abs "" ""
-norm_abs / /
-norm_abs // /
-norm_abs /// /
-norm_abs /. /
-norm_abs /./ /
-norm_abs /./.. ++failed++
-norm_abs /../. ++failed++
-norm_abs /./../.// ++failed++
-norm_abs /dir/.. /
-norm_abs /dir/sub/../.. /
-norm_abs /dir/sub/../../.. ++failed++
-norm_abs /dir /dir
-norm_abs /dir// /dir/
-norm_abs /./dir /dir
-norm_abs /dir/. /dir/
-norm_abs /dir///./ /dir/
-norm_abs /dir//sub/.. /dir/
-norm_abs /dir/sub/../ /dir/
-norm_abs //dir/sub/../. /dir/
-norm_abs /dir/s1/../s2/ /dir/s2/
-norm_abs /d1/s1///s2/..//../s3/ /d1/s3/
-norm_abs /d1/s1//../s2/../../d2 /d2
-norm_abs /d1/.../d2 /d1/.../d2
-norm_abs /d1/..././../d2 /d1/d2
+# Absolute path tests must be skipped on Windows because due to path mangling
+# the test program never sees a POSIX-style absolute path
+case $(uname -s) in
+*MINGW*)
+	;;
+*)
+	test_set_prereq POSIX
+	;;
+esac
+
+norm_path "" ""
+norm_path . ""
+norm_path ./ ""
+norm_path ./. ""
+norm_path ./.. ++failed++
+norm_path ../. ++failed++
+norm_path ./../.// ++failed++
+norm_path dir/.. ""
+norm_path dir/sub/../.. ""
+norm_path dir/sub/../../.. ++failed++
+norm_path dir dir
+norm_path dir// dir/
+norm_path ./dir dir
+norm_path dir/. dir/
+norm_path dir///./ dir/
+norm_path dir//sub/.. dir/
+norm_path dir/sub/../ dir/
+norm_path dir/sub/../. dir/
+norm_path dir/s1/../s2/ dir/s2/
+norm_path d1/s1///s2/..//../s3/ d1/s3/
+norm_path d1/s1//../s2/../../d2 d2
+norm_path d1/.../d2 d1/.../d2
+norm_path d1/..././../d2 d1/d2
+
+norm_path / / POSIX
+norm_path // / POSIX
+norm_path /// / POSIX
+norm_path /. / POSIX
+norm_path /./ / POSIX
+norm_path /./.. ++failed++ POSIX
+norm_path /../. ++failed++ POSIX
+norm_path /./../.// ++failed++ POSIX
+norm_path /dir/.. / POSIX
+norm_path /dir/sub/../.. / POSIX
+norm_path /dir/sub/../../.. ++failed++ POSIX
+norm_path /dir /dir POSIX
+norm_path /dir// /dir/ POSIX
+norm_path /./dir /dir POSIX
+norm_path /dir/. /dir/ POSIX
+norm_path /dir///./ /dir/ POSIX
+norm_path /dir//sub/.. /dir/ POSIX
+norm_path /dir/sub/../ /dir/ POSIX
+norm_path //dir/sub/../. /dir/ POSIX
+norm_path /dir/s1/../s2/ /dir/s2/ POSIX
+norm_path /d1/s1///s2/..//../s3/ /d1/s3/ POSIX
+norm_path /d1/s1//../s2/../../d2 /d2 POSIX
+norm_path /d1/.../d2 /d1/.../d2 POSIX
+norm_path /d1/..././../d2 /d1/d2 POSIX
 
 ancestor / "" -1
 ancestor / / -1
@@ -80,10 +130,10 @@ ancestor /foo/bar /:/foo:/bar/ 4
 ancestor /foo/bar /foo:/:/bar/ 4
 ancestor /foo/bar /:/bar/:/fo 0
 ancestor /foo/bar /:/bar/ 0
-ancestor /foo/bar :://foo/. 4
-ancestor /foo/bar :://foo/.:: 4
-ancestor /foo/bar //foo/./::/bar 4
-ancestor /foo/bar ::/bar -1
+ancestor /foo/bar .:/foo/. 4
+ancestor /foo/bar .:/foo/.:.: 4
+ancestor /foo/bar /foo/./:.:/bar 4
+ancestor /foo/bar .:/bar -1
 
 test_expect_success 'strip_path_suffix' '
 	test c:/msysgit = $(test-path-utils strip_path_suffix \