The problem with tinning wires that go under screw clamps is that even when the screw is done up tight the solder will slowly collapse with time and the joint comes loose. The answer is to leave the wires untinned and let the screw clamp down on the copper.

A technique I prefer is to use pins from old D connectors (the sort used for PC serial connections and so on) as a pin on the end of the wire and then screw down on that. This means that you don't end up with stray strands loose.
Here is a photo of an example ...


If you pick your old connector right they are often easy to disassemble and reclaim the pins. If the two holes on the ends are riveted over the drill out the folded over metal and the connector shell will fall apart and the pins are easily reclaimed. Other styles of shell may be harder to disassemble, but with some perseverance can be done.

If all else fails then suitable pins can be purchased from RS or Farnell/Onecall/Element14 (or whatever their current name is, they are now part of the Arrow group).

Another option if you have an appropriate crimp tool are what are sometimes known as 'boot ferrules' or sometimes just as 'ferrules' which are crimped onto the end of the wire to achieve the same end result. generally these do not go down small enough for the sort of wire we deal with though.