diff --git a/pkg/sentry/platform/systrap/filters.go b/pkg/sentry/platform/systrap/filters.go
index 0b3c620bc..fc8222cfb 100644
--- a/pkg/sentry/platform/systrap/filters.go
+++ b/pkg/sentry/platform/systrap/filters.go
@@ -72,6 +72,13 @@ func (p *Systrap) SyscallFilters() seccomp.SyscallRules {
 		},
 		unix.SYS_TGKILL: {},
 		unix.SYS_WAIT4:  {},
+		unix.SYS_SETPRIORITY: {
+			{
+				seccomp.EqualTo(unix.PRIO_PROCESS),
+				seccomp.MatchAny{},
+				seccomp.EqualTo(sysmsgThreadPriority),
+			},
+		},
 	}
 	r.Merge(p.archSyscallFilters())
 	return r
diff --git a/pkg/sentry/platform/systrap/subprocess.go b/pkg/sentry/platform/systrap/subprocess.go
index 8fdc5021c..439ca3649 100644
--- a/pkg/sentry/platform/systrap/subprocess.go
+++ b/pkg/sentry/platform/systrap/subprocess.go
@@ -1005,6 +1005,17 @@ func (s *subprocess) getSysmsgThread(tregs *arch.Registers, c *context, ac *arch
 	return s.createSysmsgThread(tregs, c, ac)
 }
 
+var sysmsgThreadPriority int
+
+func initSysmsgThreadPriority() {
+	prio, err := unix.Getpriority(unix.PRIO_PROCESS, 0)
+	if err != nil {
+		panic("unable to get current scheduling priority")
+	}
+	// Sysmsg threads are executed with a priority one lower than the Sentry.
+	sysmsgThreadPriority = 20 - prio + 1
+}
+
 // createSysmsgThread creates a new sysmsg thread.
 // If contextDecouplingExp=false, the thread starts working on the given context.
 // Otherwise the given function parameters are not used, and the thread starts
@@ -1108,6 +1119,10 @@ func (s *subprocess) createSysmsgThread(tregs *arch.Registers, c *context, ac *a
 
 	sysThread.msg.State.Set(sysmsg.ThreadStateInitializing)
 
+	if err := unix.Setpriority(unix.PRIO_PROCESS, int(p.tid), sysmsgThreadPriority); err != nil {
+		log.Warningf("Unable to change priority of a stub thread: %s", err)
+	}
+
 	// Install a pre-compiled seccomp rules for the BPF process.
 	_, err = p.syscallIgnoreInterrupt(&p.initRegs, unix.SYS_PRCTL,
 		arch.SyscallArgument{Value: uintptr(linux.PR_SET_NO_NEW_PRIVS)},
diff --git a/pkg/sentry/platform/systrap/systrap.go b/pkg/sentry/platform/systrap/systrap.go
index 4c4a9018a..e1416ae80 100644
--- a/pkg/sentry/platform/systrap/systrap.go
+++ b/pkg/sentry/platform/systrap/systrap.go
@@ -337,6 +337,8 @@ func New() (*Systrap, error) {
 		source.DecRef(nil)
 
 		globalPool.source = source
+
+		initSysmsgThreadPriority()
 	})
 
 	return &Systrap{memoryFile: mf}, nil