It also has the name Droimeann Donn Dilis. Niamh Parsons performs it on her Blackbirds and Thrushes CD. It is done half in Irish and half in English.

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I also found as "Drimindhu-deelish (o, hee hee) in Library of Congress search.

Drimindhu-deelish; an old Irish melody.

LC Control Number: unk84132596
Type of Material: Book (Print, Microform, Electronic, etc.)
Brief Description:

McDonnell, C. [from old catalog]
Drimindhu-deelish; an old Irish melody.
Baltimore, John Cole [183-?]
3 p. 33 cm.
CALL NUMBER: M1.A13 M
Copy 1
-- Request in: Performing Arts Reading Room (Madison, LM113)
-- Status: Not Charged