diff --git a/lib/Email/MIME/Header.pm b/lib/Email/MIME/Header.pm
index e2c6fea..600a1ad 100644
--- a/lib/Email/MIME/Header.pm
+++ b/lib/Email/MIME/Header.pm
@@ -56,8 +56,6 @@ sub header_str {
 
   foreach my $header (@header) {
     next unless defined $header;
-    next unless $header =~ /=\?/;
-
     _maybe_decode($_[0], \$header);
   }
   return $wanta ? @header : $header[0];
diff --git a/lib/Email/MIME/Header/AddressList.pm b/lib/Email/MIME/Header/AddressList.pm
index 311369f..497c4ea 100644
--- a/lib/Email/MIME/Header/AddressList.pm
+++ b/lib/Email/MIME/Header/AddressList.pm
@@ -8,6 +8,7 @@ use warnings;
 use Carp ();
 use Email::Address::XS;
 use Email::MIME::Encode;
+use Net::IDN::Encode;
 
 =encoding utf8
 
@@ -17,6 +18,10 @@ Email::MIME::Header::AddressList - MIME support for list of Email::Address::XS o
 
 =head1 SYNOPSIS
 
+  use utf8;
+  use Email::Address::XS;
+  use Email::MIME::Header::AddressList;
+
   my $address1 = Email::Address::XS->new('Name1' => 'address1@host.com');
   my $address2 = Email::Address::XS->new("Name2 \N{U+263A}" => 'address2@host.com');
   my $mime_address = Email::Address::XS->new('=?UTF-8?B?TmFtZTIg4pi6?=' => 'address2@host.com');
@@ -131,14 +136,20 @@ sub new_mime_groups {
     $groups[2 * $_ + 1] = [ @{$groups[2 * $_ + 1]} ];
     foreach (@{$groups[2 * $_ + 1]}) {
       next unless Email::Address::XS->is_obj($_);
-      my $decode_phrase = (defined $_->phrase and $_->phrase =~ /=\?/);
-      my $decode_comment = (defined $_->comment and $_->comment =~ /=\?/);
-      next unless $decode_phrase or $decode_comment;
+      my $phrase = $_->phrase;
+      my $comment = $_->comment;
+      my $host = $_->host;
+      my $decode_phrase = (defined $phrase and $phrase =~ /=\?/);
+      my $decode_comment = (defined $comment and $comment =~ /=\?/);
+      my $decode_host = (defined $host and $host =~ /xn--/);
+      next unless $decode_phrase or $decode_comment or $decode_host;
       $_ = ref($_)->new(copy => $_);
-      $_->phrase(Email::MIME::Encode::mime_decode($_->phrase))
+      $_->phrase(Email::MIME::Encode::mime_decode($phrase))
         if $decode_phrase;
-      $_->comment(Email::MIME::Encode::mime_decode($_->comment))
+      $_->comment(Email::MIME::Encode::mime_decode($comment))
         if $decode_comment;
+      $_->host(Net::IDN::Encode::domain_to_unicode($host))
+        if $decode_host;
     }
   }
   return $class->new_groups(@groups);
@@ -205,14 +216,20 @@ sub as_mime_string {
       if Email::MIME::Encode::_needs_mime_encode_addr($groups[2 * $_]);
     $groups[2 * $_ + 1] = [ @{$groups[2 * $_ + 1]} ];
     foreach (@{$groups[2 * $_ + 1]}) {
-      my $encode_phrase = Email::MIME::Encode::_needs_mime_encode_addr($_->phrase);
-      my $encode_comment = Email::MIME::Encode::_needs_mime_encode_addr($_->comment);
-      next unless $encode_phrase or $encode_comment;
+      my $phrase = $_->phrase;
+      my $comment = $_->comment;
+      my $host = $_->host;
+      my $encode_phrase = Email::MIME::Encode::_needs_mime_encode_addr($phrase);
+      my $encode_comment = Email::MIME::Encode::_needs_mime_encode_addr($comment);
+      my $encode_host = (defined $host and $host =~ /\P{ASCII}/);
+      next unless $encode_phrase or $encode_comment or $encode_host;
       $_ = ref($_)->new(copy => $_);
-      $_->phrase(Email::MIME::Encode::mime_encode($_->phrase, $charset))
+      $_->phrase(Email::MIME::Encode::mime_encode($phrase, $charset))
         if $encode_phrase;
-      $_->comment(Email::MIME::Encode::mime_encode($_->comment, $charset))
+      $_->comment(Email::MIME::Encode::mime_encode($comment, $charset))
         if $encode_comment;
+      $_->host(Net::IDN::Encode::domain_to_ascii($host))
+        if $encode_host;
     }
   }
   return Email::Address::XS::format_email_groups(@groups);
diff --git a/t/unicode.t b/t/unicode.t
index f6c7cc3..4efc4be 100644
--- a/t/unicode.t
+++ b/t/unicode.t
@@ -72,6 +72,8 @@ SKIP: {
     'Doy <test@example.com>', # not
     '"<look@like.address>," <test@example.com>', # address-like pattern in phrase
     '"Döy <look@like.address>," <test@example.com>', # unicode address-like pattern in phrase
+    'adam@äli.as',            # unicode host
+    'Ädam <adam@äli.as>',     # unicode phrase and host
   );
 
   for my $subject (@subjects) {
@@ -93,8 +95,13 @@ SKIP: {
       $email->header_str_set('To', $to);
       is(scalar($email->header_str('To')), $to,
          "To header is correct");
-      like($email->as_string, qr/test\@example\.com/,
-           "address isn't encoded");
+      if ($to =~ /adam/) {
+        like($email->header_raw('To'), qr/adam\@xn--li-uia.as/,
+           'To raw header is correct');
+      } else {
+        like($email->as_string, qr/test\@example\.com/,
+             "address isn't encoded");
+      }
       like($email->as_string, qr/\A\p{ASCII}*\z/,
            "email doesn't contain any non-ascii characters");
     }