My iphone just doesn't do enough but I like the compact portability....recommendations? I find that my grandsons are always moving so I get lots of blurry pics with my phone (partially because they are moving or I am whipping out my phone to capture the moment) or my subject is too far away and the zoom on an iphone just gets grainy. I would like something small enough I would frequently just toss in my bag or backpack. Taking close ups would be nice too! I would prefer not to have to buy batteries (one with its own rechargeable). What do you like?