Eukaryotic translation initiation involves preinitiation ribosomal complex 5'-to-3' directional probing of mRNA for codons suitable for starting protein synthesis. The recognition of codons as starts depends on the codon identity and on its immediate nucleotide context known as Kozak context. When the context is weak (i.e., nonoptimal), leaky scanning takes place during which a fraction of ribosomes continues the mRNA probing. We explored the relationship between the context of AUG codons annotated as starts of protein-coding sequences and the next AUG codon occurrence. We found that AUG codons downstream from weak starts occur in the same frame more frequently than downstream from strong starts. We suggest that evolutionary selection on in-frame AUGs downstream from weak start codons is driven by the advantage of the reduction of wasteful out-of-frame product synthesis and also by the advantage of producing multiple proteoforms from certain mRNAs. We confirmed translation initiation downstream from weak start codons using ribosome profiling data. We also tested translation of alternative start codons in 10 specific human genes using reporter constructs. In all tested cases, initiation at downstream start codons was more productive than at the annotated ones. In most cases, optimization of Kozak context did not completely abolish downstream initiation, and in the specific example of mRNA, the optimized start remained unproductive. Collectively, our work reveals previously uncharacterized forces shaping the evolution of protein-coding genes and points to the plurality of translation initiation and the existence of sequence features influencing start codon selection, other than Kozak context.