Since biological inventions only benefit their possessors after they work, their origins cannot be attributed to their selective effects. One proposed solution to this conundrum is that selection perfects activities that already existed in rudimentary form before they became beneficial. An example of this idea for protein origins is the promiscuity hypothesis, which claims that minor aberrant side-reactions in enzymes can be evolutionary starting points for proficient new enzymes. Another example—the junk hypothesis—claims that proteins arising from accidental expression of non-genic DNA may likewise have slight activities that, through evolutionary optimization, lead to proficient enzymes. Here, we tested these proposals by observing how the endpoint of simple evolutionary optimization depends on the starting point. Beginning with optimization of protein-like constructs in the Stylus computational model, we compared promiscuous and junk starting points, where design elements specific to the test function were completely absent, to a starting point that retained most elements of a good design (mutation having disrupted some). In all three cases, evolutionary optimization improved activities by a large factor. The extreme weakness of the original activities, however, meant even large improvements could be inconsequential. Indeed, the endpoint was itself a proficient design only in the case where this design was largely present from the outset. Laboratory optimization of ampicillin-resistance proteins derived from a natural beta lactamase produced similar results. Our junk protein here was a deletion mutant that somehow confers weak resistance without the original catalytic mechanism (much of the active site having been lost). Evolutionary optimization was unable to improve that mutant. In contrast, a comparably weak mutant that retained the active site surpassed the natural beta lactamase after six rounds of selection. So, while mutation and selection can improve the proficiency of good designs through small structural adjustments, they seem unable to convert fortuitous selectable activities into good designs.