Dwayne's advice is dead on. It works really well. The only problem I've ever had was the wire-wrap wire coming unsoldered at the top, and that was because there was another pad right next to the failed one which transferred heat up to the top. I re-did it with the wire-wrap wire wrapped between the two pads and all was well.?
I've also pulled a variation of this trick in the past when working with a part that has a flexible, but large lead (power cap) which wouldn't fit through the hole after the wire-wrap wire was in place.Take the component lead, and bend a little loop in it, which will lay flat against the top of the PCB, contacting the remaining top layer pad or trace before going through the hole. Insert remaining lead through hole, bend over so it contacts bottom layer pad / trace, solder top and bottom.?
Obviously that won't work with a lead which isn't accessible from the top after component placement. Some components can be lifted up enough to provide access and have long enough leads to pull that trick, but many don't.?