We present an improved strong-lensing analysis of Cl0024+1654 (z= 0.39) using deep Hubble Space Telescope (HST)/Advanced Camera for Surveys (ACS)/NIC3 images, based on 33 multiply-lensed images of 11 background galaxies. These are found with a model that assumes mass approximately traces light, with a low-order expansion to allow for flexibility on large scales. The model is constrained initially by the well-known five-image system (z= 1.675) and refined as new multiply-lensed systems are identified using the model. Photometric redshifts of these new systems are then used to constrain better the mass profile by adopting the standard cosmological relation between redshift and lensing distance. Our model requires only six free parameters to describe well all positional and redshift data. The resulting inner mass profile has a slope of d log M/d log r≃−0.55, consistent with new weak-lensing measurements where the data overlap, at r≃ 200 kpc/h70. The combined profile is well fitted by a high-concentration Navarro, Frenk & White (NFW) mass profile, Cvir∼ 8.6 ± 1.6, similar to other well-studied clusters, but larger than predicted with standard Λ cold dark matter (ΛCDM). A well-defined radial critical curve is generated by the model and is clearly observed at r≃ 12 arcsec, outlined by elongated images pointing towards the centre of mass. The relative fluxes of the multiply-lensed images are found to agree well with the modelled magnifications, providing an independent consistency check.