Reinforced and prestressed concrete columns with one or two layers of carbon fibre reinforced polymer (CFRP) wrap were tested to failure in axial compression. When the results were compared with the maximum load predictions of two proposed design methods, the predictions consistently underestimated actual loads. The design methods are thus conservative. A simple analysis for circular columns reveals that the confining effect of the wrap is not engaged until the concrete actually starts failing and dilating. A finite element model of a chamfered square column confirms this analysis, as do strain readings from the tests. It is shown that strength gains are not linearly related to wrap thickness. The failure mechanism suggests that design should not be based on the ultimate strength or strain of the wrap and that strength gains can be expected to reduce with increasing brittleness of the concrete and with increasing eccentricity.