diff --git a/ods/extensions/services/dashboard-api/performance_oracle.py b/ods/extensions/services/dashboard-api/performance_oracle.py
index ffd1704e93..f7a764b6ef 100644
--- a/ods/extensions/services/dashboard-api/performance_oracle.py
+++ b/ods/extensions/services/dashboard-api/performance_oracle.py
@@ -873,7 +873,7 @@ def _usable_model_memory_gb(gpu_info: Optional[GPUInfo], system_ram_gb: int | No
         return max(ram_gb * 0.55, 2.0)
     if backend in {"cpu", "none", "unknown"} or total_gb <= 0:
         ram_gb = system_ram_gb if system_ram_gb is not None else _system_ram_gb()
-        return min(max(ram_gb * 0.35, 3.0), 8.0)
+        return min(max(ram_gb, 0.0) * 0.35, 8.0)
     return total_gb
 
 
diff --git a/ods/extensions/services/dashboard-api/tests/test_model_memory.py b/ods/extensions/services/dashboard-api/tests/test_model_memory.py
index fec67d216d..1c6f567c45 100644
--- a/ods/extensions/services/dashboard-api/tests/test_model_memory.py
+++ b/ods/extensions/services/dashboard-api/tests/test_model_memory.py
@@ -81,7 +81,8 @@ def test_filename_scale_lowers_the_kv_estimate(self):
 class TestArchitectureAwareKvCache:
 
     @pytest.mark.parametrize("backend,kind,ram,vram", [
-        ("cpu", "discrete", 8, 0), ("cpu", "discrete", 32, 0),
+        ("cpu", "discrete", 4, 0), ("cpu", "discrete", 8, 0),
+        ("cpu", "discrete", 32, 0),
         ("amd", "unified", 16, 8192), ("amd", "unified", 64, 32768),
         ("nvidia", "discrete", 8, 24576),
     ])
diff --git a/ods/extensions/services/dashboard-api/tests/test_performance_oracle.py b/ods/extensions/services/dashboard-api/tests/test_performance_oracle.py
index 72080ba615..21cb580982 100644
--- a/ods/extensions/services/dashboard-api/tests/test_performance_oracle.py
+++ b/ods/extensions/services/dashboard-api/tests/test_performance_oracle.py
@@ -1541,6 +1541,28 @@ def test_pre_download_ranker_prefers_capable_8gb_model_over_bootstrap(data_dir):
     assert ranked[0]["id"] == "qwen3.5-9b-q4"
 
 
+def test_pre_download_ranker_does_not_recommend_three_gb_model_on_4gb_cpu(data_dir):
+    model = {
+        "id": "qwen3.5-2b-q4",
+        "name": "Qwen 3.5 2B",
+        "family": "qwen",
+        "gguf_file": "Qwen3.5-2B-Q4_K_M.gguf",
+        "gguf_url": "https://example.invalid/qwen3.5-2b.gguf",
+        "size_mb": 1281,
+        "vram_required_gb": 3,
+        "context_length": 65536,
+        "specialty": "Fast",
+        "llm_model_name": "qwen3.5-2b",
+    }
+
+    ranked = rank_pre_download_models(
+        [model], _gpu(name="CPU", total_mb=0, backend="cpu"),
+        profile="qwen", installable_only=True, system_ram_gb=4,
+    )
+
+    assert ranked == []
+
+
 def test_pre_download_ranker_accounts_for_long_context_kv_on_4gb_gpu(data_dir, tmp_path):
     catalog = [
         {
diff --git a/ods/scripts/select-model.py b/ods/scripts/select-model.py
index 1acab482ee..58dbe7ae4c 100644
--- a/ods/scripts/select-model.py
+++ b/ods/scripts/select-model.py
@@ -168,7 +168,9 @@ def usable_memory_gb(backend: str, memory_type: str, vram_mb: int, ram_gb: int)
         # Macs/APUs are not handed a model that technically fits but thrashes.
         return max(float(ram_gb) * 0.55, 2.0), "unified system memory"
     if backend_key in {"cpu", "none", "unknown"} or vram_mb <= 0:
-        return min(max(float(ram_gb) * 0.35, 3.0), 8.0), "system RAM"
+        # Do not floor the model budget above available headroom on small
+        # hosts. At 4 GB, a 3 GB floor leaves only 1 GB for Linux and ODS.
+        return min(max(float(ram_gb), 0.0) * 0.35, 8.0), "system RAM"
     return float(vram_mb) / 1024.0, "GPU VRAM"
 
 
diff --git a/ods/tests/test_model_selector_cpu_memory_budget.py b/ods/tests/test_model_selector_cpu_memory_budget.py
new file mode 100644
index 0000000000..c6533a5f34
--- /dev/null
+++ b/ods/tests/test_model_selector_cpu_memory_budget.py
@@ -0,0 +1,62 @@
+#!/usr/bin/env python3
+"""Exercise the production CPU model selector at Tier 0 memory limits."""
+
+import subprocess
+import sys
+from pathlib import Path
+
+
+ROOT = Path(__file__).resolve().parents[1]
+SELECTOR = ROOT / "scripts" / "select-model.py"
+CATALOG = ROOT / "config" / "model-library.json"
+
+
+def run_selector(ram_gb: int) -> subprocess.CompletedProcess[str]:
+    return subprocess.run(
+        [
+            sys.executable,
+            str(SELECTOR),
+            "--catalog",
+            str(CATALOG),
+            "--backend",
+            "cpu",
+            "--memory-type",
+            "none",
+            "--vram-mb",
+            "0",
+            "--ram-gb",
+            str(ram_gb),
+            "--profile",
+            "qwen",
+            "--tier",
+            "0",
+            "--max-size-mb",
+            "0",
+            "--host-arch",
+            "amd64",
+            "--installable-only",
+            "--env",
+        ],
+        capture_output=True,
+        text=True,
+        check=False,
+    )
+
+
+def test_four_gb_cpu_host_does_not_get_a_three_gb_model_recommendation():
+    result = run_selector(4)
+    assert result.returncode == 2, result.stdout
+    assert "no installable model fits" in result.stderr
+
+
+def test_eight_gb_cpu_host_keeps_supported_model_recommendation():
+    result = run_selector(8)
+    assert result.returncode == 0, result.stderr
+    assert 'LLM_MODEL="qwen3.5-2b"' in result.stdout
+    assert 'MAX_CONTEXT="65536"' in result.stdout
+
+
+if __name__ == "__main__":
+    test_four_gb_cpu_host_does_not_get_a_three_gb_model_recommendation()
+    test_eight_gb_cpu_host_keeps_supported_model_recommendation()
+    print("CPU model memory budget tests passed: 2")