We present a type reconstruction algorithm for SCIR , a type system for a language with syntactic control of interference. SCIR guarantees that terms of passive type do not cause any side effects, and that distinct identifiers do not interfere. A reconstruction algorithm for this type system must deal with different kinds (passive and general) and different uses of identifiers (passive and active). In particular, there may not be a unique choice of kinds for type variables. Our work extends SCIR typings with kind constraints. We show that principal type schemes exist for this extended system and outline an algorithm for computing them.