We present a new delay-based transport protocol named FLOWER, that aims at providing a Lower-than-Best-Effort (LBE) service. The objective is to propose an alternative to the Low Extra Delay Background Transport (LEDBAT) widely deployed within the official BitTorrent client. Indeed, besides its intra-fairness problem, known as latecomer unfairness, LEDBAT can be too aggressive against TCP, making it ill suited for providing LBE services over certain networks such as constrained wireless networks. By using a fuzzy controller to modulate the sending rate, FLOWER aims to solve LEDBAT issues while fulfilling the role of a LBE protocol. FLOWER operates to a modification of the standard LEDBAT protocol implementation by replacing its proportional controller by a fuzzy controller. Thanks to this modification, our simulation results show that FLOWER can carry LBE traffic in network scenarios where LEDBAT cannot while solving the latecomer unfairness problem. The presented algorithm is simple to implement and does not require complex computation that would prevent its deployment. Finally, we show that FLOWER remains compliant when used over an AQM-based network and remains LBE while not increasing the bufferbloat.