I often see the advice "use a small soldering iron" when soldering rather delicate devices. I think that most times this is actually bad advice. I've had lots of people ask me to take a crack at soldering something after they have made a mess. I usually break out a larger iron.
To solder something you need to get the joint hot enough, or you get a bad joint. To keep the heat from traveling to the semiconductors you want to solder really fast. A small iron that has to sit on the joint for several seconds to heat it to the proper soldering temperature is sending lots of heat into the circuit while you are waiting. With a large iron, already heated up hot, it takes just a quick touch and the joint is up to temperature, the solder is in and you are done.
I did one this weekend. It was a home water sensor with a brass plated rod soldered to a circuit board. It had broken loose from a cold joint by the manufacturer. The owner tried unsuccessfully to solder it back. I simply cleaned up the mess with solder wick, then using a relatively massive 40 watt iron instead of the 25 watt iron he used I soldered it in about 2 seconds flat.