Thanks all! The dealer directed me to a section of the Shure customer help website, and apparently the issue has to do with Windows 7 (and Vista) automatically knocking the microphone recording level to the maximum 100. One has to reduce it to a setting of 2, which according to the site "is about the same gain that was offered in Windows XP." This gets rid of the noise, but this does mean the Mic Gain needs to be turned up, and the test recordings all sound somewhat thin and tinny. Still fiddling about with the different levels to try to improve it (and getting good practice as John says) and will follow advice to try out in other packages.

Much appreciated,
Zoë