I will discuss recent work with Chris Soteros and Jeremy Eng on the probabilities of different knot types for self-avoiding polygons in narrow tubes of the cubic lattice. Polygons in a tube can be characterised by a finite transfer matrix, and this allows for the derivation of pattern theorems, calculation of growth rates and exact enumeration. We also develop a static Monte Carlo method which allows us to sample polygons of a given size directly from a chosen Boltzmann distribution.