@Joyce: If you measure 31" underbust, the band size you should start with is 32". The band should be pretty snug and sit low and with a new bra you should start hooking at the outermost hook. American women are known to wear their band sizes too big with their cup sizes too small. As you go down in band size, you go up in cup size. For example, if you have been wearing a 34D, the sister size is a 32DD or even a 30E/DDD.
Nordstrom carries down to 30 bands, and most brick'n'mortar department stores go down to 32 bands but not very big in the cup size. Online, lots of options are available in 30 bands and a fair number in 28 bands. Only one company that I know of makes 26" bands, Ewa Michalak in Poland.
Specialty lingerie shops in my area seem to carry larger sizes more than smaller sizes, but there's one in the East Bay and another in the South Bay that carry smaller band sizes.