Advancements in nanoscale engineering of oxide interfaces and heterostructures have led to discoveries of emergent phenomena and new artificial materials. Combining the strengths of reactive molecular-beam epitaxy and pulsed-laser deposition, we show here, with examples of Sr1+xTi1-xO3+delta, Ruddlesden-Popper phase Lan+1NinO3n+1 (n = 4), and LaAl1+yO3(1+0.5y)/SrTiO3 interfaces, that atomic layer-by-layer laser molecular-beam epitaxy (ALL-Laser MBE) significantly advances the state of the art in constructing oxide materials with atomic layer precision and control over stoichiometry. With ALL-Laser MBE we have produced conducting LaAlO3/SrTiO3 interfaces at high oxygen pressures that show no evidence of oxygen vacancies, a capability not accessible by existing techniques. The carrier density of the interfacial two-dimensional electron gas thus obtained agrees quantitatively with the electronic reconstruction mechanism.