diff --git a/docs/source/release-notes/unreleased.rst b/docs/source/release-notes/unreleased.rst
index 09b03b4..0326975 100644
--- a/docs/source/release-notes/unreleased.rst
+++ b/docs/source/release-notes/unreleased.rst
@@ -1,6 +1,10 @@
 2.x.y - 202z-aa-bb
 ------------------
 
-- *Add Items here*
+- Preserve the leading slash required by RFC 3986 when removing dot segments
+  from rootless paths, fixing resolution against bases such as
+  ``scheme:foo/bar``. See `issue #84`_.
 
 .. links below here
+
+.. _issue #84: https://github.com/python-hyper/rfc3986/issues/84
diff --git a/src/rfc3986/normalizers.py b/src/rfc3986/normalizers.py
index 79b3585..5c4ca72 100644
--- a/src/rfc3986/normalizers.py
+++ b/src/rfc3986/normalizers.py
@@ -152,13 +152,12 @@ def remove_dot_segments(s: str) -> str:
         # element
         elif output:
             output.pop()
+            # Preserve the slash that replaces '/..' when the last segment
+            # is removed, even if the original path was rootless.
+            if not output:
+                output.append("")
 
-    # If the path starts with '/' and the output is empty or the first string
-    # is non-empty
-    if s.startswith("/") and (not output or output[0]):
-        output.insert(0, "")
-
-    # If the path starts with '/.' or '/..' ensure we add one more empty
+    # If the path ends with '/.' or '/..' ensure we add one more empty
     # string to add a trailing '/'
     if s.endswith(("/.", "/..")):
         output.append("")
diff --git a/tests/test_normalizers.py b/tests/test_normalizers.py
index 87562ac..46690ec 100644
--- a/tests/test_normalizers.py
+++ b/tests/test_normalizers.py
@@ -41,6 +41,15 @@ def test_normalize_percent_characters():
     ("//a/./b/../b/%63/%7Bfoo%7D", "//a/b/%63/%7Bfoo%7D"),
     ("mid/content=5/../6", "mid/6"),
     ("/a/b/c/./../../g", "/a/g"),
+    ("foo/../baz", "/baz"),
+    ("foo/..", "/"),
+    ("foo/../", "/"),
+    ("foo/bar/../../baz", "/baz"),
+    ("foo/../../baz", "/baz"),
+    ("foo/..//baz", "//baz"),
+    ("foo//../baz", "foo/baz"),
+    ("../", ""),
+    ("../../baz", "baz"),
 ]
 
 
diff --git a/tests/test_uri.py b/tests/test_uri.py
index 4ae383c..b03572e 100644
--- a/tests/test_uri.py
+++ b/tests/test_uri.py
@@ -293,6 +293,22 @@ def test_uris_with_no_authority_with_query_only_are_absolute(
 
 
 class TestURIReferencesResolve:
+    @pytest.mark.parametrize(
+        ["relative", "expected"],
+        [
+            ("../baz", "scheme:/baz"),
+            ("..", "scheme:/"),
+            ("../../baz", "scheme:/baz"),
+            ("../baz?query#fragment", "scheme:/baz?query#fragment"),
+            ("baz", "scheme:foo/baz"),
+        ],
+    )
+    def test_resolve_with_rootless_base(self, relative, expected):
+        base = URIReference.from_string("scheme:foo/bar")
+        reference = URIReference.from_string(relative)
+
+        assert reference.resolve_with(base).unsplit() == expected
+
     def test_with_basic_and_relative_uris(self, basic_uri, relative_uri):
         R = URIReference.from_string(relative_uri)
         B = URIReference.from_string(basic_uri)