Software implementations of cryptographic algorithms often use masking schemes as a countermeasure against side channel attacks. A number of recent results show clearly the challenge of implementing masking schemes in such a way, that (unforeseen) micro-architectural effects do not cause masking flaws that undermine the intended security goal of an implementation. So far, utilising a higher-order version of the non-specific (fixed-vs-random) input test of the Test Vector Leakage Assessment (TVLA) framework has been the best option to identify such flaws. The drawbacks of this method are both its significant computation cost, as well as its inability to pinpoint which interaction of masking shares leads to the flaw. In this paper we propose a novel version, the fixed-vs-random shares test, to tackle both drawbacks. We explain our method and show its application to three case studies, where each time it outperforms its conventional TVLA counterpart. The drawback of our method is that it requires control over the shares, which, we argue, is practically feasible in the context of in-house evaluation and testing for software implementations.