We present the design and characterization of a cladding-pumped amplifier with erbium doping located in an annular region near the core. This erbium-doped fiber is proposed to reduce gain saturation, leading to smaller gain compression when compared to uniform core doping. Through numerical simulations, we first compare the performance of three fibers with different erbium doping profiles in the core or the cladding. When the doped fibers are operated at the optimum length, results show that the smaller overlap of the signal mode field with the annular erbium doping region leads to higher gain and lower saturation of the amplifier. A single-core erbium-doped fiber with an annular doping and a D-shaped cladding was fabricated. Measurements demonstrate less than 4 dB of gain compression over the C-band for input power ranging from -40 dBm to 3 dBm. Small gain compression EDFAs are of interest for applications that require input channel reconfiguration. Higher gain and saturation output power are also key issues in cladding-pumped multi-core amplifiers.