A clamp assembly mountable on a short span of structural tubing which can have any one of a broad spectrum of transverse cross-sectional shapes, sizes and vertical orientations, as found in bicycle frames and the like. Augmenting the assembly's inner and outer clamp members, so that one can use them to maintain a tight grip on the short span, is an assortment of inserts. Each insert, when deployed between the outer member's elongated flat face and the inner clamp member's midsection where it bounds a long, relatively narrow concavity, is designed to keep the clamp members from slipping sideways with respect to the compression force applied through them to the short span. Included is a two-headed insert, deployed one head at a time, as dictated by how much the short span fills said concavity and whether it extends, beyond it, perpendicularly to the elongated flat face.
