A fluid-burning lamp that delivers a fragrance(s) and is aesthetically pleasing. The fluid-burning lamp includes a fragrance-dispensing element that contains a material that slowly melts and forms a liquid pool when the lamp is lit. The slow-melting material gives the fluid-burning lamp the appearance of a traditional wax candle, when the lamp is viewed from the top. Other elements of the fluid-burning lamp include a fluid container for holding a combustible fluid to be used as fuel for the burn, and a wick assembly containing a wick having a lower portion that extends into the combustible fluid. The fluid container for holding the combustible fluid may also hold various immersions, such as, for example, fruits, colored marbles, leaves, seeds, sprigs, or flowers, in order to provide the ultimate in flexibility for home decor.