Medicines into Japan...

I know there have been several posts about medications and bringing them into Japan, but I still have a question:

Is it possible to bring in medications for such things like Gastro or other stomach bugs? I plan to get a prescription for all my med's (including panadol) and a letter from my doctor saying why I need them etc..

I will also be putting ALL of them into my 'checked baggage', not my day bag.

Should that be sufficient to pass customs? I also know that codeine and pseudophedrine are banned substances.

Thanks for the help!

we carried all our medication, and doctors letter, with us in HAND luggage in case 1.our checked luggage went missing, or 2. we needed it on the flight or before having access to checked luggage: but had a copy of the letter with copies of our other documents in our checked luggage. We took Gastrostop (over counter) and Stemetil( with prescription) with us from Australia: didn't need either, but felt better having it with us, and had no problems with customs/immigration: the politest customs/immigration in the world