It seems obvious that Apple doesn’t particularly invite mucking with the default height of the
UIPickerView, but I have found that you can achieve a change in the height of the view by taking complete control and passing a desired frame size at creation time, e.g:
smallerPicker = [[UIPickerView alloc] initWithFrame:CGRectMake(0.0, 0.0, 320.0, 120.0)];
You will discover that at various heights and widths, there are visual glitches. Obviously, these glitches would either need to be worked around somehow, or choose another size that doesn’t exhibit them.