FedEx offers next business day delivery for document and parcels between major cities in Asia via the FedEx International Priority service (if no Customs delay)
http://www.fedex.com/my/services/asiaone/overview.html

For example, today in KL you send a parcel, tomorrow the receipient in Singapore and Hongkong shall receive it by noon!

For not-so-urgent shipments, you can use FedEx International Economy service which is more economical.
http://www.fedex.com/my/services/IE/iesvcfeatures.html

All these services are backed by FedEx Money Back Guarantee programme.
http://www.fedex.com/my/services/termsandc.../guarantee.html