I believe by and large that Neapolitan pies — if they can avoid soupiness, as they did at Motorino — are the most appealing. Yet the pan pizzas at Veloce Pizzeria, which opened in the East Village a month and a half ago, pleased me every bit as much. Sara Jenkins, the chef who supervises their production, said she isn’t sure whether to call them Sicilian or grandma style. Whatever their proper tag, these denser, richer, square pies were superb. The nicely charred crust — with a dough of potato, durum and fine zero-zero flour — was firm enough to support a generous measure of toppings. Its extra-crisp edges had the salty, zingy flavor and texture of a frico. And the toppings were first-rate, the mushroom pizza showcasing a bevy of hen-of-the-woods.

Image TOPIC FOR DISCUSSION: CRISPNESS Co. in Chelsea is run by a bread baker. Credit... Evan Sung for The New York Times

I believe that firmer, less runny cheese works better most of the time, and yet the Pugliese pie at Motorino, which uses wet-centered burrata, was a masterpiece, the burrata lending the pie an opulence and creaminess.

Crisp crusts, it turns out, aren’t so difficult: most places I visited had mastered that much. But crusts that are crisp without being dry — that have some give and suppleness — are an altogether trickier matter. That’s where Lucali, for example, fell down, though the ratio of mozzarella to tomatoes on its plain pie was faultless, and the tomatoes had a beautiful, round flavor.

Crusts with character and complexity are also rare. Salvatore of SoHo, a charming restaurant whose flame-throwing coal oven gave its crusts a formidable char, was slightly disappointing on this score. The crusts were one-dimensional. And a pie that advertised sausage had precious little of it.

An attractively charred look doesn’t mean an appealingly charred taste, as Zero Otto Nove illustrated. Its pies were lovely to behold — and insipid to eat. Zero Otto Nove illustrated, too, that breathtaking ovens and grandly stated goals don’t guarantee excellence, or even enjoyment. I got almost no pleasure from the soggy pies at Kesté — including one with sausage that could have come from a Jimmy Dean’s freezer package — though Kesté, too, introduced itself as many discerning cuts above a run-of-the-mill slice joint.

Indeed, the wave of ostensibly principled pizza restaurants since 2004 has produced a mixed bag. Along the broad middle stretch of the spectrum, between undistinguished and outstanding, I’d place L’Asso, in NoLIta; Tonda, the East Village redo of the restaurant the E.U.; Toby’s Public House, in Greenwood Heights, Brooklyn, which has fine tap beers and a pubby warmth; and Luna Rossa, in Carroll Gardens, whose pies are the best in this little bunch.