diff --git a/Project.toml b/Project.toml
index f6afbd4..ad1c4d5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "SweepRunner"
 uuid = "be946ad2-3cb3-4b6e-8f7e-4a5ecc3c255b"
-version = "0.6.7"
+version = "0.6.8"
 authors = ["sota shimozono <shimozono-sota631@g.ecc.u-tokyo.ac.jp>"]
 
 [deps]
diff --git a/test/run/test_run_deadline.jl b/test/run/test_run_deadline.jl
index 14a0107..8c466bd 100644
--- a/test/run/test_run_deadline.jl
+++ b/test/run/test_run_deadline.jl
@@ -52,8 +52,16 @@ end
         keys = ParamIO.expand(v.spec)
         @test length(keys) > 1
         started = Ref(0)
-        deadline = time() + 0.3
-        work = k -> (started[] += 1; sleep(0.6); Dict{String,Any}("x" => 1))
+        # The first key runs until the deadline has passed, so the test does not depend on how long
+        # `run!` takes to hand it out — only that it is under the margin. A 0.3 s margin was not:
+        # a run-start observation takes most of a second, and on a hosted runner no key was handed
+        # out at all (started == 0).
+        deadline = time() + 5.0
+        work = k -> begin
+            started[] += 1
+            sleep(max(0.0, deadline - time()) + 0.1)
+            Dict{String,Any}("x" => 1)
+        end
         r = run!(work, v, keys; opts=RunOpts(workers=:sequential, deadline=deadline))
         @test started[] >= 1                 # the first key ran
         @test started[] < length(keys)       # later keys were not handed out
diff --git a/test/run/test_run_loop_busy.jl b/test/run/test_run_loop_busy.jl
index 75e8500..acaee9b 100644
--- a/test/run/test_run_loop_busy.jl
+++ b/test/run/test_run_loop_busy.jl
@@ -48,7 +48,11 @@ end
         @test n[] == 1                          # it ran the key
         @test DataVault.is_done(v, ks[1])       # and the campaign is complete
         @test r.done == 1
-        @test elapsed >= 3.0                    # it waited stale_after out rather than giving up
+        # It waited stale_after out rather than giving up (the bug gave up after two empty rounds,
+        # ~1 s). Less one second: DataVault writes `heartbeat=` truncated to the second, so the lock
+        # reads up to 1 s older than it is and is reclaimed up to 1 s before stale_after. Asserting
+        # the full 3.0 failed on hosted runners at 2.85 s and 2.90 s.
+        @test elapsed >= 3.0 - 1.0
     end
 end