Just going through the first two letters of the alphabet, these are the schools with fewer than about 3500 undergrads that I saw that offer an ABET-accredited form of some form of engineering (I excluded engineering technology).
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Abilene Christian (TX): About 3200 undergrads
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Alfred U (NY): About 1300 undergrads plus about 3300 undergrads from SUNY Alfred
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Anderson (IN): About 1100 undergrads
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Andrews (MI): About 1300 undergrads
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Azusa Pacific (CA): About 3300 undergrads
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Baldwin Wallace (OH): About 2700 undergrads
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Benedict (SC): About 1800 undergrads
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Benedictine (KS): About 2300 undergrads
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Bethel (MN): About 2600 undergrads
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Bethune-Cookman (FL): About 2700 undergrads, HBCU
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Bob Jones (SC): About 2700 undergrads
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U. of Bridgeport (CT): About 1600 undergrads
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Bryan (TN): About 1500 undergrads
Obviously, there are many more. Perhaps if I get more energy, I’ll continue to go through the alphabet.
With respect to a general engineering degree (vs. a specific form of engineering), there was a thread about it that may be helpful. Of course, I would love to hear more perspectives on the topic of this linked thread, too: