A laser-engravable composition comprises one or more elastomeric rubbers including at least 10 parts of one or more CLCB EPDM elastomeric rubbers, based on parts per hundred of the total weight of elastomeric rubbers (phr). The laser-engravable composition further comprises 2-30 phr of a near-infrared radiation absorber and either 1-80 phr of an inorganic, non-infrared radiation absorber filler, or a vulcanizing composition that comprises a mixture of at least two peroxides. One first peroxide has a t90 value of 1-6 minutes as measured at 160° C., and a second peroxide has a t90 value of 8-20 minutes as measured at 160° C. This laser-engravable composition can be used to form a laser-engravable layer on a compressible layer that is disposed on a substrate, and to form various flexographic printing precursors. The compressible layer can also be laser-engravable.