In this article, I examine whether sudden, big jumps in women's presence in parliament are sufficient for improving beliefs in women's ability to govern in the two cases with pre and posttest data: Iraq and Spain. I explain why big jumps lend themselves to tests of sufficiency, defend the theory confirming advantages of this analytic approach and discuss the advantages of the Iraqi and Spanish comparison. The Iraqi and Spanish tests of sufficiency include pre and posttest models of the effect of the big jump using ordinal regression analysis. The analyses are run over 5026 Iraqi respondents and 2411 Spanish respondents to surveys administered before and after the big jumps. The analysis confirms that big jumps are sufficient for improvement of beliefs in women's ability to govern in Iraq and Spain.