The control of HgI2 photodissociation is proposed as a paradigm of control of polyatomic fragmentation using sequences of optical pulses. We focus on a collinear model, with the excited electronic state surface taken from the work of Zewail and co-workers and the ground electronic state surface adapted from the work of Bernstein and co-workers. We find that, using a sequence of two Gaussian pulses with a variable delay time and dump frequency, it is possible to obtain selectivity of fragmentation in the ground electronic state ranging from 95% for three-body products (Hg + I + I) with one pulse sequence to 78% for two-body products (HgI + I) with a different sequence.