Cornett

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The cornett is the most highly prized instrument of the 16th century. It is made of wood and has fingerholes like a recorder but it is played with a mouthpiece similar to a trumpet's. Masters of the cornett are renowned for their virtuosity and are the highest paid players of the orchestra. Princes often compete for their services. On of the greatest composers of this time, Monteverdi, while court composer at Mantua, complained bitterly that his stipend was lower than that of the cornettists in his orchestra.
The fingerholes on cornetts have to be spaced rather widely apart to give clear notes, and a difficulty with the straight treble is the absence of any relief for the stretch of the lower fingers. (Photos courtesy of Jonathan M. Askey at website The London Early Music Shop - see credits)
References:

Baines, Anthony. European & American Musical Instruments. Viking Press, New York, 1966.

Buchner, Dr. Alexander (translated by Iris Urwin). Musical Instruments Through the Ages. Batchworth Press Limited, London, England, 1961.
Hindley, Geoffrey (ed.). The Larousse Encyclopedia of Music. Excalibur Books, New York, 1982.