Hey I just happened across this thread and though I should share some info for all who want to see if there is really any signal improvement.
So for the Verizon network the frequency for the cellular signal is between 800 and 1900 MHz, I think. I saw that that range can also vary more, and the reason for such a range anyway is the location of the signal. For those that live in rural or light suburban areas, a lower frequency is better and for much denser populated areas, with more buildings and stuff in the way of the signal higher frequencies are used. SO, consider first the kind of environment you are in with your phone, then for the antenna length you choose to fit that frequency. For example at 800 MHz the resonant antenna length is 375 mm to match the wavelength. But since 375 mm is way impractical, taking half, or fourths, or eighths, etc. of that length will be the best you can do with just adding simple wire in your phone. As you work up to the higher frequencies like 1900 MHz you need less wire, only 157.894 mm ideally, but again you can cut that smaller by half's each time. So for 1900 you could do a 19.73675mm wire.
Maybe this will get some people on the right track if my reasoning is correct with matching ideal antenna length to wavelength.