We study the impact that mimimum quality standards have on industry structure, trade, and welfare when firms can develop their own private standard with a higher quality than the public standard. We introduce vertical differentiation in a firm-based trade model in which firms differ in terms of their productivity and non-cooperatively select the quality and price of their product. A higher public standard increases prices set by constrained and unconstrained firms, but the effect on firms’ output is generally ambiguous for both types of firms. The most productive firms raise their private standard and enjoy higher profits at the expense of less productive firms. A public standard can increase welfare, especially when there is a high concentration of low productivity domestic firms because of a better allocation of resources.