How to achieve lower shutdown current with Serial LTE Modem?

I'm evaluating nRF9160 + Serial LTE Modem application for a battery powered device that uploads data via HTTP POST 8-12 times per day.  Since all interactions are initiated from the device its desirable to achieve a very low power level between communications.  Currently I'm sending +CFUN=0 for this state, however power measured with the nrf9160-DK is still around 2.5mW (0.5 mA @ 5V). 

What steps should I take to achieve a lower standby/quiescent power state?

Does +CPSMS help after +CFUN=0 has been sent?

Is it necessary to sleep the UART ?