We present a simple and efficient entropy coder that combines run-length and Golomb-Rice encoders. The encoder automatically switches between the two modes according to simple rules that adjust the encoding parameters based on the previous output codeword, and the decoder tracks such changes. This adaptive Run-Length/Golomb-Rice (RLGR) coder has a fast learning rate, making it suitable for many practical applications, which usually involve encoding small source blocks. We study the encoding of generalized Gaussian (GG) sources after quantization with uniform scalar quantizers with deadzone, which are good source models in multimedia data compression, for example. We show that, for a wide range of source parameters, the RLGR encoder has a performance close to that of the optimal Golomb-Rice and Exp-Golomb coders designed with knowledge of the source statistics, and in some cases the RLGR coder improves coding efficiency by 20% or more.