diff --git a/test/blackbox-tests/test-cases/melange/installed-virtual-lib-deps.t b/test/blackbox-tests/test-cases/melange/installed-virtual-lib-deps.t
index cd613f69763..e3d11a05ae1 100644
--- a/test/blackbox-tests/test-cases/melange/installed-virtual-lib-deps.t
+++ b/test/blackbox-tests/test-cases/melange/installed-virtual-lib-deps.t
@@ -16,17 +16,33 @@ The virtual library and its implementation are both Melange-only.
   >  (name vlib)
   >  (public_name repro.vlib)
   >  (modes melange)
-  >  (virtual_modules virt))
+  >  (private_modules helper leaf unused)
+  >  (virtual_modules virt other))
   > EOF
   $ cat > producer/vlib/virt.mli <<'EOF'
   > val run : unit -> int
   > EOF
+  $ cat > producer/vlib/other.mli <<'EOF'
+  > val run : unit -> int
+  > EOF
   $ cat > producer/vlib/shared.ml <<'EOF'
+  > let answer = Helper.answer + Other.run ()
+  > EOF
+  $ cat > producer/vlib/helper.ml <<'EOF'
+  > let answer = Leaf.answer
+  > EOF
+  $ cat > producer/vlib/leaf.ml <<'EOF'
   > let answer = 42
   > EOF
+  $ cat > producer/vlib/unused.ml <<'EOF'
+  > let ignored = 0
+  > EOF
 
   $ dune build --root producer @install
   $ dune install --root producer --prefix "$PWD/prefix"
+  $ test -e "$PWD/prefix/lib/repro/vlib/melange/vlib__Shared.cmt"
+  $ test -e "$PWD/prefix/lib/repro/vlib/melange/.private/vlib__Helper.cmt"
+  $ test -e "$PWD/prefix/lib/repro/vlib/melange/.private/vlib__Leaf.cmt"
 
   $ cat > consumer/dune-project <<'EOF'
   > (lang dune 3.24)
@@ -43,17 +59,49 @@ The virtual library and its implementation are both Melange-only.
   $ cat > consumer/impl/virt.ml <<'EOF'
   > let run () = Shared.answer
   > EOF
+  $ cat > consumer/impl/other.ml <<'EOF'
+  > let run () = 1
+  > EOF
   $ cat > consumer/dune <<'EOF'
   > (melange.emit
   >  (target output)
   >  (emit_stdlib false)
+  >  (compile_flags :standard --mel-cross-module-opt)
   >  (libraries impl))
   > EOF
 
   $ OCAMLPATH="$PWD/prefix/lib:$OCAMLPATH" \
-  > dune build --root consumer @melange
+  > dune build --root consumer --sandbox=symlink @melange
   Entering directory 'consumer'
   File "impl/.impl.objs/melange/_unknown_", line 1, characters 0-0:
   Error: No rule found for impl/.impl.objs/native/vlib__Shared.cmx
   Leaving directory 'consumer'
   [1]
+
+With annotations, dependency analysis should read the precise imports from the
+CMT, including private modules but excluding unused ones.
+
+  $ OCAMLPATH="$PWD/prefix/lib:$OCAMLPATH" \
+  > dune rules --root consumer --recursive --format=json --deps --display=quiet \
+  > impl/.impl.objs/melange/vlib__Virt.cmj > deps.json
+  Entering directory 'consumer'
+  Error: No rule found for impl/.impl.objs/native/vlib__Shared.cmx
+  -> required by transitive deps of vlib__Shared.impl in _build/default/impl
+  -> required by transitive deps of vlib__Virt.impl in _build/default/impl
+  Leaving directory 'consumer'
+  [1]
+  $ jq_dune -r '
+  >   [.[] | depsFilePaths
+  >    | select(endswith("vlib__Helper.cmi")
+  >             or endswith("vlib__Helper.cmj")
+  >             or endswith("vlib__Leaf.cmi")
+  >             or endswith("vlib__Leaf.cmj")
+  >             or endswith("vlib__Other.cmi")
+  >             or endswith("vlib__Other.cmj")
+  >             or endswith("vlib__Unused.cmi")
+  >             or endswith("vlib__Unused.cmj")
+  >             or endswith("vlib__Virt.cmi")
+  >             or endswith("vlib__Virt.cmj"))
+  >    | select(startswith("_build/default/impl/.impl.objs/melange/"))]
+  >   | unique[]
+  > ' deps.json