If you're not rooted, check out Clean Master or DU Battery Saver on Google Play.
These apps manage your phone in the background and they are relatively small in terms of app size.
If you're rooted and are using a custom ROM check their threads for any issues or try another ROM.
I'm currently using the Odexed Blue Themed ROM which is basically stock except for a few tweaks including theme changed to primarily blue.
I was using the Minin ROM before which is a stripped down version of the Stock ROM.
Proud supporter of XDA.
Proud Owner of the Samsung Galaxy Note 3 as of 10/27/2013.
Former User of the Samsung Galaxy Note II and the HTC Evo Series including the Original 4G and 4G LTE phones.
But you knew that already.