No Room for 2nd floor bathtup trap

I am renovating my 2nd floor bathroom and am replacing the 2nd floor bathtub. The tub i replaced was not installed correctly so i can;t compare it to that. But when i went to put the new tub in i ran into a problem, i don't have enough depth (i have 2x6 joists) for the drain and trap. short of not putting in the trap at all, is there something i can do to fit a drain and trap within the depth permitted by the 2x6 floor joist?

2X6 is a pretty small floor joist. Was this house built to code? Have a general contractor look at it and see it will even hold the weight of a tub.

Assuming your floor is strong enough and you continue, you must have a trap. The trap prevents sewer gases from coming back into the house. It would be really ugly if there was no trap - both from a danger (flamable - methane) and health/smell point of view. If the floor is okay, you may just have to live with part of the trap sticking out through the ceiling downstairs, or you could put the bathtub up on a pedestal to achieve the necessary depth.