Paraxial solves are used to maintain some first-order property of an optical system (such as image position or paraxial ray angle) at a predetermined value by adjusting the curvature or thickness for a specified surface. Solves simplify the specification of an optical system and remove side constraints from the merit function for image quality. The application of paraxial solves is referenced to the program style of ACCOS V. The various types of paraxial solves allowed by ACCOS V are discussed first. Several new solves are intro-duced. One of these is a yy solve that permits optical systems to be specified by a yy diagram. Another new solve sets the curvature of a surface to maintain a specified value of paraxial ray height at the following surface. Examples of application of these solves are given. Familiarity with ACCOS V is assumed.