SMPS Design Transformer Core Selection
Any core without a gap will have its maximum value of permeability. Adding a small gap can significantly reduce the permeability of the gapped-core and this reduces peak flux density significantly for the same number of turns and current flowing.

It's all contained in this formula, B = \$H\cdot\mu\$ 

where B is flux density, H is magnetic field strength and mu is the actual magnetic permeability of the core (or core with gap).

H is the ampere-turns of the excitation coil (primary) divided by distance around the core. If you add a gap that reduces B by 2 then, you should add turns back-on to restore the inductance of the primary. The beauty is that inductance is related to turns squared so if B halves (due to the gap) then you need to increase turns by 1.414 to restore the inductance.

But, this increases H by 1.414 so the halved value of B increases by 1.414 to 70.7% of where it was originally.

So now you have a transformer with a gap that has exactly the same inductance as before but only 70.7% of the peak flux density (at the expense of more turns). If you can fit the extra turns on and reducing B to 70% is acceptable then you have a simple solution.

Of course you'll now have bigger copper losses and you might be fighting a battle that cannot be cheaply won. Keeping the turns as low as you can is a big help - having no more turns than necessary is the trick.