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Thirty three words put D first and L third, and only vowels ever appear in the second box. That is unusual enough to be the first thing to use.
E takes the second box in eleven words and O in ten. A, I and U take four each. No consonant appears there at all, across all thirty three words.
So the second box is a shortlist rather than a search. That is the cheapest narrowing available and it is worth spending the first guess on.
DELAY, DELTA and DELVE are the reachable words in the E branch. DOLLS, DOLES and DOLOR carry the O branch.
Together those two hold twenty one of the thirty three, so most of the page is one of them. Working out which comes before anything else.
DALES, DALLY, DILLY and DULLY sit outside both. None is common, but between them they cover three different second letters, which makes any one of them a better splitter than another DEL guess.
Eleven words repeat a letter, which is a high share, and nearly all of them double the L. DOLLY, DOLLS, DALLY, DILLY, DILLS, DULLY and DULLS all do it, so a visible repeat leaves you a shortlist rather than an answer.
Both are common and they differ in two boxes, so the pair narrows well. DELTA also tests T in the fourth box, which few words here take.
Six words do, and most are the doubled L forms like DOLLY and DULLY. The LY ending accounts for most of them.
It appears on this list as a musical direction meaning softly. DOLCI is its plural form and both are word game entries.