Full-flow T-bar and ball penetrometer tests are often used to measure intact and remoulded soil strengths, with the latter determined after several large amplitude displacement cycles. In offshore design the remoulded soil strength is often the governing design parameter during installation of subsea infrastructure, whilst a ‘cyclic strength’ applies for the less severe operational cyclic loading. This paper utilises T-bar penetrometer tests to measure both remoulded and cyclic strengths, where the latter is determined via a new test protocol involving cycles between load rather than displacement limits. The tests use kaolin clay and a reconstituted carbonate silt and involve three cyclic phases with intervening consolidation periods. The results demonstrate the important and beneficial role of consolidation, with the loss in strength due to remoulding sometimes surpassed by the strength recovery from consolidation. The most significant gains in strength, to 2.5 times the initial value, were measured in the load-controlled cyclic tests. These data demonstrate a novel way to characterise undrained cyclic strength, taking advantage of consolidation to reduce conservatism.