We have cut up a pepper in many ways: carefully cutting out the stem, spilling out the seeds and then proceeding to chop; cutting the whole top off and then slicing the pepper; cutting the pepper in half, washing away the seeds before chopping.
We recently learned (from a cooking show) a new way of chopping a pepper and I was quite impressed after trying it out. One simply holds the pepper on its head (upside down) and starts slicing from the tip, down to the stem. If one cuts carefully to avoid the core, the white inner skin can also be cut away. When complete, all of the seeds remain stuck to the inner core. With three of four slices, the stem, seeds, core, inner white skin are removed and once can now nicely chop the tasty bit of the pepper.