In crystal structures that lack inversion symmetry, parity is no longer a meaningful label. Without parity to enforce that the superconducting pairing state be either singlet or triplet, and with terms allowed in the Hamiltonian that would normally be forbidden by symmetry, a wide variety of highly unconventional behaviour is possible. Some such behaviour has been observed, but in (typically Ce-based) f-electron systems where poorly-understood noncentrosymmetric physics can be difficult to distinguish from the underlying poorly-understood f-electron physics. To help clarify the effect of a lack of inversion symmetry, we have been investigating the H-T phase diagram and specific heat of noncentrosymmtric superconductors that lack f-electrons. I will report our findings on two systems, CaTSi3 (T = Ir, Pt) and Li2(Pd,Pt)3B.