Two new schemes for computing molecular total atomization energies (TAEs) and/or heats of formation (Delta H-f(degrees)) of first- and second-row compounds to very high accuracy are presented. The more affordable scheme, W1 (Weizmann-1) theory, yields a mean absolute error of 0.30 kcal/mol and includes only a single, molecule-independent, empirical parameter. It requires CCSD (coupled cluster with all single and double substitutions) calculations in spdf and spdfg basis sets, while CCSD(T) (i.e., CCSD with a quasiperturbative treatment of connected triple excitations) calculations are only required in spd and spdf basis sets. On workstation computers and using conventional coupled cluster algorithms, systems as large as benzene can be treated, while larger systems are feasible using direct coupled cluster methods. The more rigorous scheme, W2 (Weizmann-2) theory, contains no empirical parameters at all and yields a mean absolute error of 0.23 kcal/mol, which is lowered to 0.18 kcal/mol for molecules dominated by dynamical correlation. It involves CCSD calculations in spdfg and spdfgh basis sets and CCSD(T) calculations in spdf and spdfg basis sets. On workstation computers, molecules with up to three heavy atoms can be treated using conventional coupled cluster algorithms, while larger systems can still be treated using a direct CCSD code. Both schemes include corrections for scalar relativistic effects, which are found to be vital for accurate results on second-row compounds.