diff --git a/internal/agent/agent_test.go b/internal/agent/agent_test.go
index a3dc052..8bf4929 100644
--- a/internal/agent/agent_test.go
+++ b/internal/agent/agent_test.go
@@ -400,11 +400,16 @@ func TestHeartbeatKeepsNodeAlive(t *testing.T) {
 	n, _ := h.inv.Get("n1")
 	first := n.LastSeen
 
-	time.Sleep(200 * time.Millisecond)
-	n, _ = h.inv.Get("n1")
-	if !n.LastSeen.After(first) {
-		t.Error("heartbeats are not refreshing LastSeen; the node would be declared lost")
+	// Waited for rather than slept through: four heartbeat intervals was not
+	// always enough on a loaded runner for one to have landed.
+	deadline := time.Now().Add(3 * time.Second)
+	for time.Now().Before(deadline) {
+		if n, _ = h.inv.Get("n1"); n.LastSeen.After(first) {
+			return
+		}
+		time.Sleep(20 * time.Millisecond)
 	}
+	t.Error("heartbeats are not refreshing LastSeen; the node would be declared lost")
 }
 
 func TestStartAndStopShardEndToEnd(t *testing.T) {
diff --git a/internal/agent/supervisor/supervisor_test.go b/internal/agent/supervisor/supervisor_test.go
index 1fb998d..3039a7a 100644
--- a/internal/agent/supervisor/supervisor_test.go
+++ b/internal/agent/supervisor/supervisor_test.go
@@ -243,7 +243,9 @@ func TestWaitReadyTimeoutIncludesLogs(t *testing.T) {
 	if err != nil {
 		t.Fatal(err)
 	}
-	time.Sleep(100 * time.Millisecond) // let the line be captured
+	eventually(t, 3*time.Second, "the line was never captured", func() bool {
+		return strings.Contains(strings.Join(sh.Logs(10), "\n"), "CUDA out of memory")
+	})
 
 	err = s.WaitReady(t.Context(), sh, "http://x", "m", 200*time.Millisecond)
 	if err == nil {
@@ -295,7 +297,10 @@ func TestLogsAreCaptured(t *testing.T) {
 	if err != nil {
 		t.Fatal(err)
 	}
-	time.Sleep(400 * time.Millisecond)
+	eventually(t, 3*time.Second, "not every line arrived", func() bool {
+		l := strings.Join(sh.Logs(10), "\n")
+		return strings.Contains(l, "line1") && strings.Contains(l, "line2") && strings.Contains(l, "line3")
+	})
 
 	logs := strings.Join(sh.Logs(10), "\n")
 	for _, want := range []string{"line1", "line2", "line3"} {
@@ -372,11 +377,11 @@ func TestStateFileRemovedOnExit(t *testing.T) {
 
 	sh, _ := s.Start(t.Context(), "a", engines.ShardSpec{}, shellCommand("exit 0"))
 	waitState(t, sh, Failed, 3*time.Second)
-	time.Sleep(50 * time.Millisecond)
-
-	if _, err := os.Stat(s.statePath("a")); !os.IsNotExist(err) {
-		t.Error("the state file outlived the process; a later scan would find a dead orphan")
-	}
+	eventually(t, 3*time.Second,
+		"the state file outlived the process; a later scan would find a dead orphan", func() bool {
+			_, err := os.Stat(s.statePath("a"))
+			return os.IsNotExist(err)
+		})
 }
 
 // --- state machine and ring buffer ---
@@ -743,7 +748,9 @@ func TestWaitAliveFailsOnEarlyExit(t *testing.T) {
 	if err := s.WaitAlive(t.Context(), sh); err == nil {
 		t.Fatal("a worker that died immediately was reported ready")
 	}
-	if d := time.Since(start); d > 1500*time.Millisecond {
+	// Below AliveGrace (5s), which is what waiting it out would take; the
+	// headroom is for a loaded runner, where 1.5s was sometimes not enough.
+	if d := time.Since(start); d > 4*time.Second {
 		t.Errorf("waited %v for a process that had already exited", d)
 	}
 }
@@ -827,3 +834,17 @@ func TestAWorkersOnlyProcessWaitsForTheLeader(t *testing.T) {
 		t.Errorf("the worker started after %v, before the leader was listening", d)
 	}
 }
+
+// eventually waits for cond, failing with msg if it does not hold within
+// limit. Sleeping a fixed time and then checking measured the machine the
+// test ran on, and a loaded CI runner under the race detector lost that race.
+func eventually(t *testing.T, limit time.Duration, msg string, cond func() bool) {
+	t.Helper()
+	deadline := time.Now().Add(limit)
+	for !cond() {
+		if time.Now().After(deadline) {
+			t.Fatal(msg)
+		}
+		time.Sleep(10 * time.Millisecond)
+	}
+}
diff --git a/internal/router/admission/admission_test.go b/internal/router/admission/admission_test.go
index 7d9dd02..be4987f 100644
--- a/internal/router/admission/admission_test.go
+++ b/internal/router/admission/admission_test.go
@@ -42,14 +42,20 @@ func newController(t *testing.T, cfg Config, sat SaturationFunc) *Controller {
 
 func TestAdmitsImmediatelyWhenIdle(t *testing.T) {
 	s := &fixedSat{}
-	c := newController(t, testConfig(), s.fn)
+	// A queue that is looked at every ten seconds, so a request that went
+	// through it rather than the fast path would take that long. A bound of
+	// 50ms against a 1ms tick measured the machine the test ran on, and a
+	// loaded CI runner under the race detector was slower than that.
+	cfg := testConfig()
+	cfg.Interval = 10 * time.Second
+	c := newController(t, cfg, s.fn)
 
 	start := time.Now()
 	lease, err := c.Acquire(t.Context(), Request{Model: "m", Band: "bronze"})
 	if err != nil {
 		t.Fatal(err)
 	}
-	if d := time.Since(start); d > 50*time.Millisecond {
+	if d := time.Since(start); d > 2*time.Second {
 		t.Errorf("idle admission took %v; the fast path is not being used", d)
 	}
 	lease.Release()
@@ -131,8 +137,13 @@ func TestQueuedRequestAdmittedWhenSaturationDrops(t *testing.T) {
 		done <- err
 	}()
 
-	// Give it time to actually queue, then open the gate.
-	time.Sleep(50 * time.Millisecond)
+	// Wait for it to actually queue, then open the gate. Waited for, not
+	// slept through: on a loaded runner 50ms was sometimes not long enough
+	// for the goroutine to have been scheduled at all.
+	deadline := time.Now().Add(2 * time.Second)
+	for c.Depths()[3].Depth != 1 && time.Now().Before(deadline) {
+		time.Sleep(5 * time.Millisecond)
+	}
 	if d := c.Depths(); d[3].Depth != 1 {
 		t.Fatalf("expected 1 queued bronze request, got %+v", d)
 	}
diff --git a/internal/router/scrape/llamacpp_test.go b/internal/router/scrape/llamacpp_test.go
index a03e23b..93df598 100644
--- a/internal/router/scrape/llamacpp_test.go
+++ b/internal/router/scrape/llamacpp_test.go
@@ -175,7 +175,10 @@ func TestABrokenContractIsReportedOnceAndLoudly(t *testing.T) {
 	in := endpoint.Info{ID: "e1", URL: srv.URL, Engine: "vllm", Models: []string{"m"}}
 	reg.Replace([]endpoint.Info{in})
 
-	p := NewPoller(reg, Config{Interval: 20 * time.Millisecond, Timeout: 10 * time.Millisecond},
+	// A generous timeout: a scrape that timed out would be reported as
+	// unreachable, and the violation reported again once it answered — two
+	// warnings where the test counts one, on a slow runner only.
+	p := NewPoller(reg, Config{Interval: 20 * time.Millisecond, Timeout: 2 * time.Second},
 		slog.New(cap))
 	ctx, cancel := context.WithCancel(context.Background())
 	defer cancel()