We present a compact iodine-stabilized laser system at 633 nm, based on a distributed-feedback laser diode. Within a footprint of 27×15cm2, the system provides 5 mW of frequency-stabilized light from a single-mode fiber. Its performance was evaluated in comparison to Cs clocks representing primary frequency standards, realizing the SI unit Hz via an optical frequency comb. With the best suited absorption line, the laser reaches a fractional frequency instability below 10-10 for averaging times above 10 s. The performance was investigated at several iodine lines, and a model was developed to describe the observed stability on the different lines.