Singular values of multiple eta-quotients for ramified primes

We determine the conditions under which singular values of multiple eta-quotients of square-free level, not necessarily prime to six, yield class invariants; that is, algebraic numbers in ring class fields of imaginary-quadratic number fields. We show that the singular values lie in subfields of the ring class fields of index 2(k'-1) when k' >= 2 primes dividing the level are ramified in the imaginary-quadratic field, which leads to faster computations of elliptic curves with prescribed complex multiplication. The result is generalised to singular values of modular functions on X-0(+)(p) for p prime and ramified.