  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
a graph on the plane cannot have more edges than vertices. We prove the
Conjecture for thrackle drawings all of whose vertices lie on the boundaries of
$d \le 3$ connected domains in the complement of the drawing. We also give a
detailed description of thrackle drawings corresponding to the cases when $d=2$
(annular thrackles) and $d=3$ (pants thrackles).
