This makes it less efficient - in this case, 18/60 chance of having to redraw, versus 4/60. Taking the modulus of the largest range you can leaves less residue (what lutusp is alluding to, without realizing others are describing a simple way of getting an exact uniform distribution).

If you want to make it more efficient (in terms of entropy used), you need to save the 1-of-prime (eg bits, trits, etc) that have been successfully chosen (uniformly). For example, with 6 children and an 8 sided die (3 bits), a roll of 6 or 7 would narrow the choices to only children 0-2 or 3-5 respectively. Your subsequent rolls could then be done with a 4 sided die.