Abstract Interval-based possibilistic logic is a flexible setting tending standard possibilistic logic such that each logical expression is associated with a sub-interval of [0, 1 This paper focuses on the fundamental issue of conditioning in the interval-based possibilistic setting. The part of the paper first proposes a set of natural propert that an interval-based conditioning operator should satisfy. We then give a natural and safe definition for conditioning an interval-based possibility distribution. Thi definition is based on applying standard min-based or product-based conditioning on the set of all associated compatible possibility distributions. We analyze the obtained posterior distributions and provide a precise char acterization of lower and upper endpoints of the intervals associated with interpretations. The second part of the paper provides an equivalent syntactic computation of interval-based conditioning when interval-based distributions are compactly encoded by means of interval-based possibilistic knowledge bases. We show that intervalbased conditioning is achieved without extra computational cost comparing to conditioning standard possibilis tic knowledge bases.