diff --git a/constraint.go b/constraint.go
index 1d88090..8d7b24a 100644
--- a/constraint.go
+++ b/constraint.go
@@ -46,6 +46,8 @@ func init() {
 		">=": {op: greaterThanEqual, f: constraintGreaterThanEqual},
 		"<=": {op: lessThanEqual, f: constraintLessThanEqual},
 		"~>": {op: pessimistic, f: constraintPessimistic},
+		"^":  {op: caret, f: constraintCaret},
+		"~":  {op: tilde, f: constraintTilde},
 	}
 
 	ops := make([]string, 0, len(constraintOperators))
@@ -221,7 +223,9 @@ const (
 	lessThan         operator = '<'
 	greaterThanEqual operator = '≥'
 	lessThanEqual    operator = '≤'
-	pessimistic      operator = '~'
+	pessimistic      operator = '≳'
+	caret            operator = '^'
+	tilde            operator = '~'
 )
 
 func constraintEqual(v, c *Version) bool {
@@ -288,3 +292,31 @@ func constraintPessimistic(v, c *Version) bool {
 	// If nothing has rejected the version by now, it's valid
 	return true
 }
+
+func constraintCaret(v, c *Version) bool {
+	if !prereleaseCheck(v, c) || v.LessThan(c) {
+		return false
+	}
+
+	if v.segments[0] != c.segments[0] {
+		return false
+	}
+
+	return true
+}
+
+func constraintTilde(v, c *Version) bool {
+	if !prereleaseCheck(v, c) || v.LessThan(c) {
+		return false
+	}
+
+	if v.segments[0] != c.segments[0] {
+		return false
+	}
+
+	if v.segments[1] != c.segments[1] && c.si > 1 {
+		return false
+	}
+
+	return true
+}
diff --git a/constraint_test.go b/constraint_test.go
index a6f90d7..17ee339 100644
--- a/constraint_test.go
+++ b/constraint_test.go
@@ -78,6 +78,19 @@ func TestConstraintCheck(t *testing.T) {
 		{">= 2.1.0-a", "2.1.1-beta", false},
 		{">= 2.1.0-a", "2.1.0", true},
 		{"<= 2.1.0-a", "2.0.0", true},
+		{"^1.1", "1.1.1", true},
+		{"^1.1", "1.2.3", true},
+		{"^1.1", "2.1.0", false},
+		{"^1.1.2", "1.1.1", false},
+		{"^1.1.2", "1.1.2", true},
+		{"^1.1.2", "1.1.2.3", true},
+		{"~1", "1.3.5", true},
+		{"~1", "2.1.0", false},
+		{"~1.1", "1.1.1", true},
+		{"~1.1", "1.2.3", false},
+		{"~1.1.2", "1.1.1", false},
+		{"~1.1.2", "1.1.2", true},
+		{"~1.1.2", "1.1.2.3", true},
 	}
 
 	for _, tc := range cases {