Given a regular, uncountable cardinal κ, it is often desirable to be able to construct objects of size κ⁺ using approximations of size less than κ. Historically, such constructions have often been carried out with the help of a (κ, 1)-morass and/or a ◇(κ)-sequence. We present a framework for carrying out such constructions using ◇(κ) and a weakening of Jensen's principle ◻_κ. Our framework takes the form of a forcing axiom, SDFA(P_κ). We show that SDFA(P_κ) follows from the conjunction of ◇(κ) and our weakening of ◻_κ and, if κ is the successor of an uncountable cardinal, that SDFA(P_κ) is in fact equivalent to this conjunction. We also show that, for an infinite cardinal λ, SDFA(P_λ⁺) implies the existence of a λ⁺-complete λ⁺⁺-Souslin tree. This implies that, if λ is an uncountable cardinal, 2^λ = λ⁺, and Souslin's Hypothesis holds at λ⁺⁺, then λ⁺⁺ is a Mahlo cardinal in L, improving upon an old result of Shelah and Stanley. This is joint work with Assaf Rinot.