TPS61299: Minimizing Input Current Ripple

I am trying to design a boost converter module that will take a 1.6 V input source, with a capacity on the order of 1 mAh, and boost the output voltage to 1.8 or 3.3 V.  The output load current for my application will be between 1-10 mA.  However, the capacity of my input battery power source reduces significantly when there are large current spikes.  I am currently using the TPS61299, and on the data sheet, it says that it operates with a fixed inductor ripple current of 350 mA.  When I test my battery source with the TPS61299 evaluation board, I find that the battery life is significantly lower than expected, likely due to these current spikes.  Is there a way I can reduce the input current ripple, ideally at least by an order of magnitude?  I am open to using other boost converter devices outside of the TPS61299 if necessary.