Although powerful (2.8 W) blue emission at 473 nm was recently reported, the design of low-cost compact and efficient 473 nm source failed so far. We have theoretically and experimentally analyzed the operation of a simple 2.1 mm long microchip assembly pumped by a 100x1 μm laser diode and found several ways to improve the efficiency of such a laser. As a first result, we achieved high beam quality (M2<1.2) 40 mW CW operation @ 473 nm with less than 900 mW launched power (5% efficiency) and small low-frequency (10Hz-20 kHz) noise. Multi-frequency operation however led to high-frequency noise (green problem). To our best knowledge, this is the highest efficiency obtained with a linear cavity. In this paper, we model and measure thermal lensing, pump, 946 nm and 473 nm beam size and power evolution within the MCA. Nd concentration was left unoptimized in previously reported experiments to its standard value (1.1%). Optimum Nd concentration is shown to generally be greater than 1% and is compatible with efficient low-noise single-frequency operation.