diff --git a/pkg/seccomp/seccomp.go b/pkg/seccomp/seccomp.go
index c7503f2cc..fc36efa23 100644
--- a/pkg/seccomp/seccomp.go
+++ b/pkg/seccomp/seccomp.go
@@ -199,6 +199,10 @@ func ruleViolationLabel(ruleSetIdx int, sysno uintptr, idx int) string {
 	return fmt.Sprintf("ruleViolation_%v_%v_%v", ruleSetIdx, sysno, idx)
 }
 
+func ruleLabel(ruleSetIdx int, sysno uintptr, idx int, name string) string {
+	return fmt.Sprintf("rule_%v_%v_%v_%v", ruleSetIdx, sysno, idx, name)
+}
+
 func checkArgsLabel(sysno uintptr) string {
 	return fmt.Sprintf("checkArgs_%v", sysno)
 }
@@ -223,6 +227,19 @@ func addSyscallArgsCheck(p *bpf.ProgramBuilder, rules []Rule, action linux.BPFAc
 					p.AddStmt(bpf.Ld|bpf.Abs|bpf.W, seccompDataOffsetArgHigh(i))
 					p.AddJumpFalseLabel(bpf.Jmp|bpf.Jeq|bpf.K, high, 0, ruleViolationLabel(ruleSetIdx, sysno, ruleidx))
 					labelled = true
+				case GreaterThan:
+					labelGood := fmt.Sprintf("gt%v", i)
+					high, low := uint32(a>>32), uint32(a)
+					// assert arg_high < high
+					p.AddStmt(bpf.Ld|bpf.Abs|bpf.W, seccompDataOffsetArgHigh(i))
+					p.AddJumpFalseLabel(bpf.Jmp|bpf.Jge|bpf.K, high, 0, ruleViolationLabel(ruleSetIdx, sysno, ruleidx))
+					// arg_high > high
+					p.AddJumpFalseLabel(bpf.Jmp|bpf.Jeq|bpf.K, high, 0, ruleLabel(ruleSetIdx, sysno, ruleidx, labelGood))
+					// arg_low < low
+					p.AddStmt(bpf.Ld|bpf.Abs|bpf.W, seccompDataOffsetArgLow(i))
+					p.AddJumpFalseLabel(bpf.Jmp|bpf.Jgt|bpf.K, low, 0, ruleViolationLabel(ruleSetIdx, sysno, ruleidx))
+					p.AddLabel(ruleLabel(ruleSetIdx, sysno, ruleidx, labelGood))
+					labelled = true
 				default:
 					return fmt.Errorf("unknown syscall rule type: %v", reflect.TypeOf(a))
 				}
diff --git a/pkg/seccomp/seccomp_rules.go b/pkg/seccomp/seccomp_rules.go
index 29eec8db1..84c841d7f 100644
--- a/pkg/seccomp/seccomp_rules.go
+++ b/pkg/seccomp/seccomp_rules.go
@@ -49,6 +49,9 @@ func (a AllowAny) String() (s string) {
 // AllowValue specifies a value that needs to be strictly matched.
 type AllowValue uintptr
 
+// GreaterThan specifies a value that needs to be strictly smaller.
+type GreaterThan uintptr
+
 func (a AllowValue) String() (s string) {
 	return fmt.Sprintf("%#x ", uintptr(a))
 }
diff --git a/pkg/seccomp/seccomp_test.go b/pkg/seccomp/seccomp_test.go
index 353686ed3..abbee7051 100644
--- a/pkg/seccomp/seccomp_test.go
+++ b/pkg/seccomp/seccomp_test.go
@@ -340,6 +340,54 @@ func TestBasic(t *testing.T) {
 				},
 			},
 		},
+		{
+			ruleSets: []RuleSet{
+				{
+					Rules: SyscallRules{
+						1: []Rule{
+							{
+								GreaterThan(0xf),
+								GreaterThan(0xabcd000d),
+							},
+						},
+					},
+					Action: linux.SECCOMP_RET_ALLOW,
+				},
+			},
+			defaultAction: linux.SECCOMP_RET_TRAP,
+			specs: []spec{
+				{
+					desc: "GreaterThan: Syscall argument allowed",
+					data: seccompData{nr: 1, arch: linux.AUDIT_ARCH_X86_64, args: [6]uint64{0x10, 0xffffffff}},
+					want: linux.SECCOMP_RET_ALLOW,
+				},
+				{
+					desc: "GreaterThan: Syscall argument disallowed (equal)",
+					data: seccompData{nr: 1, arch: linux.AUDIT_ARCH_X86_64, args: [6]uint64{0xf, 0xffffffff}},
+					want: linux.SECCOMP_RET_TRAP,
+				},
+				{
+					desc: "Syscall argument disallowed (smaller)",
+					data: seccompData{nr: 1, arch: linux.AUDIT_ARCH_X86_64, args: [6]uint64{0x0, 0xffffffff}},
+					want: linux.SECCOMP_RET_TRAP,
+				},
+				{
+					desc: "GreaterThan2: Syscall argument allowed",
+					data: seccompData{nr: 1, arch: linux.AUDIT_ARCH_X86_64, args: [6]uint64{0x10, 0xfbcd000d}},
+					want: linux.SECCOMP_RET_ALLOW,
+				},
+				{
+					desc: "GreaterThan2: Syscall argument disallowed (equal)",
+					data: seccompData{nr: 1, arch: linux.AUDIT_ARCH_X86_64, args: [6]uint64{0x10, 0xabcd000d}},
+					want: linux.SECCOMP_RET_TRAP,
+				},
+				{
+					desc: "GreaterThan2: Syscall argument disallowed (smaller)",
+					data: seccompData{nr: 1, arch: linux.AUDIT_ARCH_X86_64, args: [6]uint64{0x10, 0xa000ffff}},
+					want: linux.SECCOMP_RET_TRAP,
+				},
+			},
+		},
 	} {
 		instrs, err := BuildProgram(test.ruleSets, test.defaultAction)
 		if err != nil {