Although  there  is  growing  interest  in  measuring  integrated  information  in  computational  and cognitive systems, current methods for doing so in practice are computationally unfeasible.  Existing and  novel  integration  measures  are  investigated  and  classified  by  various  desirable  properties.   A simple taxonomy of Φ-measures is presented where they are each characterized by their choice of factorization  method  (5  options),  choice  of  probability  distributions  to  compare  (3 × 4  options) and choice of measure for comparing probability distributions (7 options).  When requiring the Φ- measures to satisfy a minimum of attractive properties, these hundreds of options reduce to a mere handful, some of which turn out to be identical.  Useful exact and approximate formulas are derived that can be applied to real-world data from laboratory experiments without posing unreasonable computational demands.