How can we avoid double billing counter contracts after renewal?

We renew our contracts 15 days prior to expiration and we load counter values 2-5 days into the next period for the previous period.

We find that the last period for the original contract is also being billed during the first billing period for the renewed contract, how can we avoid this?

It seems these readings need to be disabled on the renewed contract.

Example:

Contract XXX

01Aug2014 - 31Jul2015

Contract XXX 16Jul2015 created as the renewal

Counter values loaded for 31Jul2015 on 02Aug2015 and they appear on both contracts...how can we prevent billing the July counter value more than once since it appears on multiple contracts?