diff --git a/pkg/kubelet/cm/cpuset/cpuset.go b/pkg/kubelet/cm/cpuset/cpuset.go
index de72ba25756..24330e5a9e3 100644
--- a/pkg/kubelet/cm/cpuset/cpuset.go
+++ b/pkg/kubelet/cm/cpuset/cpuset.go
@@ -301,7 +301,7 @@ func Parse(s string) (CPUSet, error) {
 	ranges := strings.Split(s, ",")
 
 	for _, r := range ranges {
-		boundaries := strings.Split(r, "-")
+		boundaries := strings.SplitN(r, "-", 2)
 		if len(boundaries) == 1 {
 			// Handle ranges that consist of only one element like "34".
 			elem, err := strconv.Atoi(boundaries[0])
@@ -319,6 +319,11 @@ func Parse(s string) (CPUSet, error) {
 			if err != nil {
 				return NewCPUSet(), err
 			}
+			if start > end {
+				return NewCPUSet(), fmt.Errorf("invalid range %q (%d >= %d)", r, start, end)
+			}
+			// start == end is acceptable (1-1 -> 1)
+
 			// Add all elements to the result.
 			// e.g. "0-5", "46-48" => [0, 1, 2, 3, 4, 5, 46, 47, 48].
 			for e := start; e <= end; e++ {
diff --git a/pkg/kubelet/cm/cpuset/cpuset_test.go b/pkg/kubelet/cm/cpuset/cpuset_test.go
index c77ab8b7543..d79748df506 100644
--- a/pkg/kubelet/cm/cpuset/cpuset_test.go
+++ b/pkg/kubelet/cm/cpuset/cpuset_test.go
@@ -323,7 +323,7 @@ func TestCPUSetString(t *testing.T) {
 }
 
 func TestParse(t *testing.T) {
-	testCases := []struct {
+	positiveTestCases := []struct {
 		cpusetString string
 		expected     CPUSet
 	}{
@@ -332,9 +332,12 @@ func TestParse(t *testing.T) {
 		{"1,2,3,4,5", NewCPUSet(1, 2, 3, 4, 5)},
 		{"1-5", NewCPUSet(1, 2, 3, 4, 5)},
 		{"1-2,3-5", NewCPUSet(1, 2, 3, 4, 5)},
+		{"5,4,3,2,1", NewCPUSet(1, 2, 3, 4, 5)},  // Range ordering
+		{"3-6,1-5", NewCPUSet(1, 2, 3, 4, 5, 6)}, // Overlapping ranges
+		{"3-3,5-5", NewCPUSet(3, 5)},             // Very short ranges
 	}
 
-	for _, c := range testCases {
+	for _, c := range positiveTestCases {
 		result, err := Parse(c.cpusetString)
 		if err != nil {
 			t.Fatalf("expected error not to have occurred: %v", err)
@@ -343,4 +346,20 @@ func TestParse(t *testing.T) {
 			t.Fatalf("expected string \"%s\" to parse as [%v] (got [%v])", c.cpusetString, c.expected, result)
 		}
 	}
+
+	negativeTestCases := []string{
+		// Non-numeric entries
+		"nonnumeric", "non-numeric", "no,numbers", "0-a", "a-0", "0,a", "a,0", "1-2,a,3-5",
+		// Incomplete sequences
+		"0,", "0,,", ",3", ",,3", "0,,3",
+		// Incomplete ranges and/or negative numbers
+		"-1", "1-", "1,2-,3", "1,-2,3", "-1--2", "--1", "1--",
+		// Reversed ranges
+		"3-0", "0--3"}
+	for _, c := range negativeTestCases {
+		result, err := Parse(c)
+		if err == nil {
+			t.Fatalf("expected parse failure of \"%s\", but it succeeded as \"%s\"", c, result.String())
+		}
+	}
 }