Be aware of the country's several restrictions on the importation of goods.
Again, we need to add some perspective. Customs officers in Singapore don't go through all the luggage that comes in. For you to get stung, they would have to pick your bags for scanning or for a manual search. The amount of precaution you want to exercise is up to you.
First of all, there's a mandatory death penalty for drug trafficking, or for carrying explosives and firearms without a licence.
Prescription drugs may also raise a flag. Travellers are advised to carry their prescriptions with them. Any medication that contains strong narcotics, like diazepam or codeine, need prior approval from the Health Sciences Authority.
Objects that resemble weapons, like novelty cigarette lighters and toy guns, can be considered a violation of customs laws. Even non-lethal items like kitchen knives, diving blades, empty cartridge shells and handcuffs - kinky ones with pink lace included - could get you into trouble. In one famous case, a woman was arrested because the little missiles on a toy plane she carried were mistaken for bullets.
If you want to transport a weapon or military souvenirs into Singapore, even if on transit, you'll need prior permission.
Pirated material, like movies, CDs, and software are illegal. If you are that way inclined, you'll have to ship home all those bootleg DVDs you got in Thailand or leave them behind, unless you want to risk a 1000 SGD fine per disk. (Besides, bootlegs suck anyway)
Pornography is outlawed. Even what might be simple considered risque in your country could be treated as porn, so it's best to not take chances.
There are some duty-free allowances on alcohol, except if you're bringing it in from Malaysia. But there are no allowances for tobacco. All cigarettes legally sold in the country must be stamped "SDPC". Although one open pack will likely be tolerated, you could be fined 500 SDG per sealed pack.
Finally, there is a total ban on Jehovah's Witnesses and the Unification Church. Any publication from these two faiths are considered illegal.
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