In case you are not aware, Amazon do provide free shipping to Singapore through its AmazonGlobal Saver program. Your order has to be above US$125 (S$156) and every item in your order has to qualify for AmazonGlobal Saver.
As long as one of your items doesn’t qualify for AmazonGlobal Saver, your whole order doesn’t qualify. Anything single item that is bigger than 18 x 11 x 8 inches (45cm x 28cm x 20cm) or 20 pounds (9kg) will not qualify for AmazonGlobal Saver. I also heard that if your single item costs more than US$50 it will not qualify for AmazonGlobal Saver as well.