Let Y be a closed, orientable 3-manifold with Heegaard genus 2. We prove that if H1(Y ; Z) has order 1, 3, or 5, then there is a representation π1(Y ) → SU(2) with non-abelian image. Similarly, if H1(Y ; Z) has order 2 then we find a non-abelian representation π1(Y ) → SO(3). We also prove that a knot K in S³ is a trefoil if and only if there is a unique conjugacy class of irreducible representations π1(S³\ K) → SU(2) sending a fixed meridian to (i 0 0 −i)