Preventing Voltage Dips


I am trying to power an GSM module from a 3.6V lithium battery via a couple
of FETS and I am finding that the modem won't connect when the battery
voltage drops to about 3.6V. I have measured the voltage at the modem with
my scope and I have noticed that the voltage dips about 800mV during its
transmissions bursts. At first I thought it was a problem with my FET's but
when I measured right back at the battery it was still dropping around
500mV. I have about 1200uF on the modem and I have noticed that the more
capacitance I use, the better it is but I would prefer not too use big
capacitors on this design. Does anyone know of any better ways to get
around this? The Current spikes are around 2A for about 500uS every 5mS.

Best regards,

Adrian Hamilton