diff --git a/DESIGN_COMPLETE.md b/DESIGN_COMPLETE.md
index 4796b77..36bd848 100644
--- a/DESIGN_COMPLETE.md
+++ b/DESIGN_COMPLETE.md
@@ -108,9 +108,14 @@ Final separator is `/` and the final component has no `.`. We complete a path
 - `/<frag>` → **root names**: the page-root (package) and lib-root (library)
   names from `Show.scan` (`/odoc`, `/odoc.model`, `/ocaml-compiler`, …),
   filtered by `frag`.
-- `/<root>/<frag>` → **units/pages in that root**: directory entries of the
-  root's dir (from `scan`'s `page_roots`/`lib_roots`), i.e. the `.odoc` files'
-  names (capitalised; `page-`/`impl-` handled) and sub-directories.
+- `/<root>/<sub>/…/<frag>` → **entries of a directory under the root**: the
+  first segment resolves to the root's dir (from `scan`'s
+  `page_roots`/`lib_roots`); any further segments are literal sub-directories
+  beneath it (`/odoc/deprecated/` → `odoc/odoc/deprecated`). The directory's
+  entries are offered: `.odoc` files' names (capitalised units; `page-` →
+  page name; `impl-`/`asset-` skipped) and sub-directories, hidden (`__`) names
+  filtered. So pages nested under a package (`/odoc/deprecated/index`) complete
+  at any depth.
 
 When the final component *does* contain a `.` (`/odoc.model/Foo.ba`), the last
 separator is that `.`, so it falls through to case 1 with a path-qualified
@@ -192,7 +197,7 @@ needed for v1.
 |---|---|---|
 | `X.Y.frag`, `kind-X.kind-frag` | yes | the core case; reuses `show` |
 | `/frag` (root names) | yes | from `scan` roots |
-| `/root/frag` (units in root) | yes | directory listing |
+| `/root/…/frag` (entries under a root, any depth) | yes | directory listing |
 | `/root/Unit.frag` (path + dotted) | yes | path-qualified resolve + children |
 | bare `frag` (top-level) | last | units + `Stdlib` members; broad |
 | `./…`, `//…` (relative paths) | no | no "current unit" in `complete` |
diff --git a/lib/complete.ml b/lib/complete.ml
index 101639e..158a21a 100644
--- a/lib/complete.ml
+++ b/lib/complete.ml
@@ -201,30 +201,42 @@ let complete_root_names scan ~stem ~comp =
   |> List.sort_uniq compare
   |> List.map (fun n -> stem ^ n)
 
-let complete_in_root scan ~stem ~comp ~root =
-  match List.assoc_opt root (scan.Refs.page_roots @ scan.Refs.lib_roots) with
-  | None -> []
-  | Some dir -> (
-      match Bos.OS.Dir.contents dir with
-      | Error _ -> []
-      | Ok entries ->
-          List.filter_map
-            (fun p ->
-              let is_dir =
-                match Bos.OS.Dir.exists p with Ok b -> b | _ -> false
-              in
-              entry_name p ~is_dir)
-            entries
-          |> List.filter (fun n -> (not (hidden n)) && starts_with ~prefix:comp n)
-          |> List.sort_uniq compare
-          |> List.map (fun n -> stem ^ n))
+(* List a directory's entries (units, pages, sub-dirs) as path segments. *)
+let complete_dir dir ~stem ~comp =
+  match Bos.OS.Dir.contents dir with
+  | Error _ -> []
+  | Ok entries ->
+      List.filter_map
+        (fun p ->
+          let is_dir =
+            match Bos.OS.Dir.exists p with Ok b -> b | _ -> false
+          in
+          entry_name p ~is_dir)
+        entries
+      |> List.filter (fun n -> (not (hidden n)) && starts_with ~prefix:comp n)
+      |> List.sort_uniq compare
+      |> List.map (fun n -> stem ^ n)
 
 let complete_path scan ~stem ~comp =
+  (* [stem] is the path up to and including the last [/]. The first segment is a
+     root name ([odoc], [odoc.model], …); any further segments are literal
+     sub-directories beneath it ([/odoc/deprecated/] -> odoc/odoc/deprecated). *)
   match String.split_on_char '/' stem with
-  | [ ""; "" ] -> complete_root_names scan ~stem ~comp (* "/" *)
-  | [ ""; root; "" ] when root <> "" ->
-      complete_in_root scan ~stem ~comp ~root (* "/root/" *)
-  | _ -> [] (* "//", "./", deeper: out of scope *)
+  | "" :: "" :: _ -> [] (* "//…" current package: out of scope *)
+  | "" :: rest -> (
+      match List.filter (( <> ) "") rest with
+      | [] -> complete_root_names scan ~stem ~comp (* "/" *)
+      | root :: subs -> (
+          match
+            List.assoc_opt root (scan.Refs.page_roots @ scan.Refs.lib_roots)
+          with
+          | None -> []
+          | Some base ->
+              if List.exists (fun s -> s = "." || s = "..") subs then []
+              else
+                let dir = List.fold_left (fun d s -> Fpath.(d / s)) base subs in
+                complete_dir dir ~stem ~comp))
+  | _ -> [] (* "./…" relative, or no leading slash: out of scope *)
 
 (* {1 Splitting and dispatch} *)