We present an improved strong-lensing analysis of Cl0024+1654 ( z =0.39 ) using deep HST/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 5-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 6 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 \simeq - 0.55 , consistent with new weak-lensing measurements where the data overlap , at r \simeq 200 kpc/ h _ { 70 } . The combined profile is well fitted by a high concentration NFW mass profile , C _ { vir } \sim 8.6 \pm 1.6 , similar to other well studied clusters , but larger than predicted with standard \Lambda CDM . A well defined radial critical curve is generated by the model and is clearly observed at r \simeq 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 .