Roger,
By the sounds of it, you are using soft solder, not a hard silver solder.
This is where us Brits get very confused over your terminology.
We call what you call silver solder, soft solder, used for plumbing and joints that don't require much strength. Soft soldering is usually frowned upon by the model engineering community, purely because of it's distinct lack of strength, we would only really use that if we had to caulk something, say a brass or copper fuel tank, or fixing multiple parts together so that they can be machined as one unit, then split apart again, say for making split bearings.
Our silver solder is, I think, what you would call silver braze. This is used where very strong joints are required on copper based alloys and steels.
In the US, I think everyone and his dog must make solders and fluxes, and so confusion reigns when you start to talk with brand names, as each seems to have it's own 'world beating' properties.
We normally only refer to it as hard (silver solder) or soft (plumbers solder) soldering, so the same confusion isn't present.
All we need to do for hard soldering is choose the melt range and flux, which over here, the most popular flux seems to be Tenacity 5, which seems to cope with everything from copper to stainless steel. There are lots of other brands, but they all basically work the same way. For soft soldering, almost anything that will do the job without being expensive, I tend to use non leaded solder and it's relevant flux.
John