What's the application? I'm skeptical that the effort and bulk of anything like the western union splice is worth the effort versus a basic lap joint for the vast majority of cases. Assuming both are done half-decently, anyway, and the splice is protected/reinforced with heatshrink at least. But it depends on the materials being used and the application/environment. Proper strain relief of the transitions between the splice and the parent wire on either end is important in any case, particularly for stranded wire which also requires making sure the solder doesn't wick too far along the wire. Wherever the solder ends, the wire strands will be susceptible to breakage as the wire flexes. Similarly, reinforcing the splice TOO much -- for example by using some really stiff heatshrink -- can just move the stress concentration problem from the end of the solder joint to the end of the heatshrink. Mechanically supporting the wires to either side of the splice can also help.
Not sure where I developed the poor technique of the way I've done it. Usually I tin both ends but seldom do I get a nice cacoon of smooth solder and keep meaning to ask the opinion of others..
Are you using flux? IME, a liquid flux that can get into the strands works best, especially if the wires aren't in great shape. Flux and tin each wire end, then flux them again before soldering. At that point getting a well-formed joint is mostly a matter of iron temperature and timing -- you need to put enough heat into the joint to get the solder to flow and wet out properly, but not so much heat or for so long that you burn off all of the flux.
If you're soldering stranded wire a lot, a solder pot is a really worthwhile investment, makes the tinning step faster, easier, and much more consistent.
One technique I keep forgetting to implement is cutting both wires (say a positive and negative) different lengths. This way I can solder both, but the solder connections are at different points eliminating the possibility of the strands poking through and shorting (usually I put a piece of heat shrink over each solder connection and a larger one over both of them). If the solder connections are at different points, then the other wire is protected by the insulation too.
You can sometimes save some bulk by only putting heatshrink on one of the two wires before putting the larger piece over both. The one small piece will be adequate to insulate the one wire from the other, although it doesn't provide as much mechanical/environmental protection (eg against moisture ingress into the wire) if that's important.