diff --git a/litellm/llms/anthropic/common_utils.py b/litellm/llms/anthropic/common_utils.py
index 735a001e343..cb50df64301 100644
--- a/litellm/llms/anthropic/common_utils.py
+++ b/litellm/llms/anthropic/common_utils.py
@@ -186,13 +186,15 @@ def _fetch_anthropic_models_page(
 def _fetch_anthropic_model_ids(
     api_base: str, headers: Mapping[str, str], after_id: str | None, pages_left: int
 ) -> tuple[str, ...]:
-    if pages_left <= 0:
-        raise Exception(f"Anthropic /v1/models did not terminate within {_MODEL_LIST_PAGE_CAP} pages.")
-    page: Final = _fetch_anthropic_models_page(api_base, headers, after_id)
-    page_ids: Final = tuple(entry.id for entry in page.data)
-    if not page.has_more or page.last_id is None:
-        return page_ids
-    return page_ids + _fetch_anthropic_model_ids(api_base, headers, page.last_id, pages_left - 1)
+    collected: tuple[str, ...] = ()  # rebind-ok: accumulates one page of ids per iteration
+    cursor: str | None = after_id  # rebind-ok: advances to each page's last_id
+    for _ in range(max(pages_left, 0)):
+        page: Final = _fetch_anthropic_models_page(api_base, headers, cursor)
+        collected += tuple(entry.id for entry in page.data)
+        if not page.has_more or page.last_id is None:
+            return collected
+        cursor = page.last_id
+    raise Exception(f"Anthropic /v1/models did not terminate within {_MODEL_LIST_PAGE_CAP} pages.")
 
 
 class AnthropicModelInfo(BaseLLMModelInfo):
diff --git a/litellm/llms/anthropic/wif.py b/litellm/llms/anthropic/wif.py
index 03340c0e084..4be1a1e7ae1 100644
--- a/litellm/llms/anthropic/wif.py
+++ b/litellm/llms/anthropic/wif.py
@@ -275,13 +275,17 @@ def _strip_chat_suffix(base: str) -> str:
 
 def _strip_path_suffixes(path: str) -> str:
     """Drop the chat-surface suffixes a deployment base may carry, so every tier derives the same
-    token URL. Recursion depth is bounded by the path's own segment count."""
-    trimmed: Final = path.rstrip("/")
-    shortened: Final = next(
-        (trimmed.removesuffix(suffix) for suffix in _CHAT_BASE_SUFFIXES if trimmed.endswith(suffix)),
-        trimmed,
-    )
-    return trimmed if shortened == trimmed else _strip_path_suffixes(shortened)
+    token URL. Each pass removes at most one suffix, so the loop is bounded by the segment count."""
+    trimmed = path.rstrip("/")  # rebind-ok: fixed-point strip, one suffix per pass
+    while True:
+        shortened: Final = next(
+            (trimmed.removesuffix(suffix) for suffix in _CHAT_BASE_SUFFIXES if trimmed.endswith(suffix)),
+            trimmed,
+        )
+        if shortened == trimmed:
+            return trimmed
+        # Re-strip: a doubled suffix leaves a trailing slash that would stop the next match.
+        trimmed = shortened.rstrip("/")
 
 
 def _config_value(litellm_params: Mapping[str, object] | None, param_key: str, env_name: str) -> str | None:
diff --git a/tests/test_litellm/proxy/pass_through_endpoints/test_llm_pass_through_endpoints.py b/tests/test_litellm/proxy/pass_through_endpoints/test_llm_pass_through_endpoints.py
index 7e48a1563e5..6e54bf49a3b 100644
--- a/tests/test_litellm/proxy/pass_through_endpoints/test_llm_pass_through_endpoints.py
+++ b/tests/test_litellm/proxy/pass_through_endpoints/test_llm_pass_through_endpoints.py
@@ -3967,6 +3967,11 @@ class TestAnthropicProxyRouteCallerAuthHeaders:
         ):
             monkeypatch.delenv(name, raising=False)
 
+        # A sibling test leaving SERVER_ROOT_PATH set re-prefixes the passthrough route, so
+        # /anthropic/... stops resolving and the request 404s before any header is built.
+        # Pin it so this class asserts on headers rather than on ambient state.
+        monkeypatch.delenv("SERVER_ROOT_PATH", raising=False)
+
     def _enable_wif(self, monkeypatch) -> None:
         from litellm.llms.anthropic import common_utils as anthropic_common_utils
         from litellm.llms.anthropic.wif import aget_anthropic_wif_token