  Koll\'ar's conjecture states that a complex projective surface $S$ with
quotient singularities and with $H^2(S,\bbQ)\cong \bbQ$ should be rational if
its smooth part $S^0$ is simply connected.
  We confirm the conjecture under the additional condition that the exceptional
divisor in a minimal resolution of $S$ has at most 3 components over each
singular point of $S$.
