A thrackle is a drawing of a graph in which each pair of edges meets
precisely once. Conway's Thrackle Conjecture asserts that a thrackle drawing of
graph on the plane cannot have more edges than vertices. We prove the
for thrackle drawings all of whose vertices lie on the boundaries of $d\leq 3$
domains in the complement of the drawing. We also give a detailed description
thrackle drawings corresponding to the cases when $d = 2$ (annular
thrackles) and $d = 3$ (pair of pants thrackles).