diff --git a/examples/server/server.cpp b/examples/server/server.cpp
index 8cb8d0033f7d9..1b4961d425122 100644
--- a/examples/server/server.cpp
+++ b/examples/server/server.cpp
@@ -1321,17 +1321,24 @@ struct server_slot {
             && are_lora_equal(lora, other_slot.lora);
     }
 
+    //  There are two caps on the budge of a single request:
+    //  * [params.n_predict]
+    //  * [global_params.n_predict]
+    // This function returns true if the request is not limited by either of them.
     bool has_budget(const common_params & global_params) {
         if (params.n_predict == -1 && global_params.n_predict == -1) {
             return true; // limitless
         }
+        n_remaining = INT32_MAX;
 
-        n_remaining = -1;
+        // The request or server have specified limits on the number of tokens to generate.
+        if ((params.n_predict >= 0) || (global_params.n_predict  >= 0)) {
+            n_remaining = std::min(n_remaining, params.n_predict - n_decoded);
+        }
 
-        if (params.n_predict != -1) {
-            n_remaining = params.n_predict - n_decoded;
-        } else if (global_params.n_predict != -1) {
-            n_remaining = global_params.n_predict - n_decoded;
+        // The request or server have limits based on the context window.
+        if (params.n_predict == -2 || global_params.n_predict == -2) {
+            n_remaining = std::min(n_remaining, n_ctx - n_decoded);
         }
 
         return n_remaining > 0; // no budget
diff --git a/examples/server/tests/unit/test_completion.py b/examples/server/tests/unit/test_completion.py
index 0ed5b99bef4e4..532c08597c7ab 100644
--- a/examples/server/tests/unit/test_completion.py
+++ b/examples/server/tests/unit/test_completion.py
@@ -143,6 +143,7 @@ def test_consistent_result_same_seed(n_slots: int):
 def test_different_result_different_seed(n_slots: int):
     global server
     server.n_slots = n_slots
+    server.n_predict = -1
     server.start()
     last_res = None
     for seed in range(4):
@@ -150,6 +151,7 @@ def test_different_result_different_seed(n_slots: int):
             "prompt": "I believe the meaning of life is",
             "seed": seed,
             "temperature": 1.0,
+            "n_predict": -1,
             "cache_prompt": False,  # TODO: remove this once test_cache_vs_nocache_prompt is fixed
         })
         if last_res is not None:
@@ -426,3 +428,18 @@ def test_cancel_request():
     time.sleep(1) # wait for HTTP_POLLING_SECONDS
     res = server.make_request("GET", "/slots")
     assert res.body[0]["is_processing"] == False
+
+
+def test_context_window_sized_completion():
+    server = ServerPreset.tinyllama2()
+    server.n_ctx = 16
+    server.n_predict = -1
+    server.start()
+    res = server.make_request("POST", "/completion", data={
+        "n_predict": -2,
+        "prompt": "The 50 states in the US are ",
+    })
+    assert res.status_code == 200
+    assert res.body["timings"]["predicted_n"] == server.n_ctx
+    assert res.body["stop_type"] == "limit"
+    assert type(res.body["has_new_line"]) == bool