Experimental evidence is produced to show that it is reasonable to assign a unique strength to all soils when at their respective liquid limits, and to redefine the plastic limit as the water content at which the strength is 100 times that at the liquid limit. Combining these assumptions with ideas of critical state soil mechanics it is then possible to relate the compression index of the remoulded soil to its plasticity index, and to suggest a unique relation between remoulded strength and liquidity index, irrespective of actual values of liquid and plastic limits. Field data from the Gulf of Mexico and from the North Sea are presented in support of these relations. The predictions of strength are best for overconsolidated clays, having water contents near the plastic limit.Recently in the United Kingdom the cone penetrometer has become the recommended test for determination of the liquid limit, in preference to the Casagrande test. Having redefined the plastic limit it would be logical to use the cone penetrometer to determine this too, by using cones with different weights. Experimental data are shown to illustrate and support this proposal.