We present a compact iodine-stabilized laser system at 633 nm, based on a distributed-feedback laser diode. Within a footprint of $27times 15$ cm$^2$ 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.
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