diff --git a/validate_email/email_address.py b/validate_email/email_address.py
index 52e768f..3e32a4f 100644
--- a/validate_email/email_address.py
+++ b/validate_email/email_address.py
@@ -1,3 +1,5 @@
+from typing import Optional
+
 from idna.core import IDNAError, encode
 
 from .exceptions import AddressFormatError
@@ -22,7 +24,7 @@ class EmailAddress(object):
             raise AddressFormatError
 
         # Convert internationalized domain name into the ACE encoding
-        if self._domain.startswith('[') and self._domain.endswith(']'):
+        if self.domain_literal_ip:
             self._ace_domain = self._domain
         else:
             try:
@@ -46,6 +48,16 @@ class EmailAddress(object):
         """
         return self._domain
 
+    @property
+    def domain_literal_ip(self) -> Optional[str]:
+        """
+        If the domain part of the email address is a literal IP address
+        enclosed in brackets, that IP address (without the brakcets) is
+        returned. Otherwise, `None` is returned.
+        """
+        if self._domain.startswith('[') and self._domain.endswith(']'):
+            return self._domain[1:-1]
+
     @property
     def ace(self) -> str:
         'The ASCII-compatible encoding for the email address.'
diff --git a/validate_email/mx_check.py b/validate_email/mx_check.py
index 3e99c6f..b0242c4 100644
--- a/validate_email/mx_check.py
+++ b/validate_email/mx_check.py
@@ -109,8 +109,11 @@ def mx_check(
     """
     host = helo_host or gethostname()
     from_address = from_address or email_address
-    mx_records = _get_mx_records(
-        domain=email_address.domain, timeout=dns_timeout)
+    if email_address.domain_literal_ip:
+        mx_records = [email_address.domain_literal_ip]
+    else:
+        mx_records = _get_mx_records(
+            domain=email_address.domain, timeout=dns_timeout)
     return _check_mx_records(
         mx_records=mx_records, smtp_timeout=smtp_timeout, helo_host=host,
         from_address=from_address, email_address=email_address)
diff --git a/validate_email/regex_check.py b/validate_email/regex_check.py
index eb4335a..b12d6fb 100644
--- a/validate_email/regex_check.py
+++ b/validate_email/regex_check.py
@@ -35,16 +35,16 @@ def regex_check(address: EmailAddress) -> bool:
     if not USER_REGEX.match(address.user):
         raise AddressFormatError
 
-    # Validate domain part: a) hostname.
-    if HOST_REGEX.match(address.ace_domain):
-        return True
+    # Validate domain part.
+    if address.domain_literal_ip:
+        literal_match = LITERAL_REGEX.match(address.ace_domain)
+        if literal_match is None:
+            raise AddressFormatError
+        if not _validate_ipv46_address(literal_match[1]):
+            raise AddressFormatError
+    else:
+        if HOST_REGEX.match(address.ace_domain) is None:
+            raise AddressFormatError
 
-    # Validate domain part: b) literal IP address.
-    literal_match = LITERAL_REGEX.match(address.ace_domain)
-    if literal_match:
-        ip_address = literal_match.group(1)
-        if _validate_ipv46_address(ip_address):
-            return True
-
-    # Domain part not successfully validated.
-    raise AddressFormatError
+    # All validations successful.
+    return True