Pretty much the prototypic commutative Banach algebra is the convolution algebra l_1. As befits a semisimple commutative Banach algebra, l_1 has very many closed ideals. But if one imposes a radical weight - considering the radical convolution algebra l_1(w) for a radical weight w - the only obvious or “standard” ideals are the ideals J_n consisting of functions supported on the interval [n,1). It is a beautiful result of Marc Thomas, however, that nonstandard ideals exist, for certain choices of the weight w. This pioneering example has been modified for various purposes by Read, Dales et al. But if the weight is well behaved, all the ideals are standard. The best general result in this direction is by Domar. This good behaviour sometimes spills over from the l_1 situation to that of some closely related operator algebras; a fact used in the recent collaboration of Blecher and Read.