We demonstrate the feasibility of the floating zone growth of an incongruently melting compound, Eu-substituted LSCO (La_1.66Eu_0.2Sr_0.14CuO₄), without a presintered solvent, using the laser-assisted floating zone technique. We show that the application of laser heating with a high-temperature gradient (over 1500 °C/cm) stabilizes the molten zone above the peritectic temperature of the compound in the area of the phase system, where both the solid and liquid phases coexist in the thermodynamic equilibrium, even for highly porous feed rods. This approach resulted in the successful obtention of single-crystal samples. The main advantage of this technique is that it does not require knowledge of the corresponding phase diagram to obtain single crystals of incongruently melting compounds.