diff --git a/ilsp/bicep_lsp/modules.py b/ilsp/bicep_lsp/modules.py
index 920591a..b6b0e88 100644
--- a/ilsp/bicep_lsp/modules.py
+++ b/ilsp/bicep_lsp/modules.py
@@ -67,9 +67,14 @@ def _load_catalog() -> list[dict[str, Any]]:
                 for mod_path, info in modules_raw.items():
                     versions = info.get("versions", ["latest"])
                     name = mod_path.split("/")[-1] if "/" in mod_path else mod_path
+                    # ref_path: what the user writes after 'br/modules:' in a .bicep file.
+                    # bicepconfig modulePath "bicep" means Bicep prepends "bicep/" to the
+                    # registry path automatically, so strip that prefix here.
+                    ref_path = mod_path.removeprefix("bicep/")
                     modules.append({
                         "name": name,
                         "path": mod_path,
+                        "ref_path": ref_path,  # e.g. "modules/appservice", "util/types"
                         "versions": versions,
                         "latest": versions[-1] if versions else "latest",
                         "registry": registry,
@@ -97,8 +102,13 @@ class BicepModuleCatalog:
 
     @classmethod
     def _iac_param_map(cls, module_name: str) -> dict[str, dict[str, Any]]:
-        """Return {param_name: {description, required, type}} from IAC source catalog."""
-        iac_mod = cls._iac.get(module_name, {})
+        """Return {param_name: {description, required, type}} from IAC source catalog.
+
+        IAC catalog is keyed by bare module name (last path segment), so strip any
+        path prefix (e.g. 'modules/appservice' → 'appservice').
+        """
+        bare_name = module_name.split("/")[-1]
+        iac_mod = cls._iac.get(bare_name, {})
         return {p["name"]: p for p in iac_mod.get("params", [])}
 
     @classmethod
@@ -112,12 +122,24 @@ class BicepModuleCatalog:
                 return mod
         return None
 
+    @classmethod
+    def get_module_by_ref(cls, ref_path: str) -> dict[str, Any] | None:
+        """Look up a module by the path that appears after 'br/modules:' in a .bicep file.
+
+        Matches both new-style ('modules/appservice', 'util/types') and old-style
+        bare names ('appservice') so completions work regardless of module version.
+        """
+        for mod in cls._modules:
+            if mod["ref_path"] == ref_path or mod["name"] == ref_path:
+                return mod
+        return None
+
     @classmethod
     def as_completion_items(cls) -> list[dict[str, Any]]:
         """Module name completions — shown when typing a module reference string."""
         items = []
         for mod in cls._modules:
-            ref = f"br/modules:{mod['path']}:{mod['latest']}"
+            ref = f"br/modules:{mod['ref_path']}:{mod['latest']}"
             items.append({
                 "label": mod["name"],
                 "kind": 9,  # Module
@@ -140,7 +162,7 @@ class BicepModuleCatalog:
     @classmethod
     def version_completion_items(cls, module_name: str) -> list[dict[str, Any]]:
         """Version completions for a specific module (newest first)."""
-        mod = cls.get_module_by_name(module_name)
+        mod = cls.get_module_by_ref(module_name)
         if not mod:
             return []
         schema = mod.get("schema", {})
@@ -180,7 +202,7 @@ class BicepModuleCatalog:
         has_open_quote: bool = False,
     ) -> list[dict[str, Any]]:
         """Enum/allowed-value completions for a specific param (e.g. principalType, environmentType)."""
-        mod = cls.get_module_by_name(module_name)
+        mod = cls.get_module_by_ref(module_name)
         allowed: list[str] = []
 
         if mod:
@@ -224,7 +246,7 @@ class BicepModuleCatalog:
     @classmethod
     def param_completion_items(cls, module_name: str, version: str) -> list[dict[str, Any]]:
         """Param completions for a specific module+version combination."""
-        mod = cls.get_module_by_name(module_name)
+        mod = cls.get_module_by_ref(module_name)
         if not mod:
             return []
         schema = mod.get("schema", {})
diff --git a/tests/test_proxy.py b/tests/test_proxy.py
index 5220b1d..fff9e32 100644
--- a/tests/test_proxy.py
+++ b/tests/test_proxy.py
@@ -31,9 +31,11 @@ def _completion_response(items: list) -> dict:
 
 def _make_module(name, versions=None, schema=None):
     versions = versions or ["1.0.0", "latest"]
+    path = f"bicep/modules/{name}"
     return {
         "name": name,
-        "path": f"bicep/modules/{name}",
+        "path": path,
+        "ref_path": f"modules/{name}",  # what appears after 'br/modules:' in bicep files
         "versions": versions,
         "latest": versions[-1],
         "registry": "iactemplatereg.azurecr.io",