He wins the ball unobtrusively with sound positioning and sharp tackling, and uses it intelligently with swift and accurate passing.
"We need Enciso," says veteran defender Carlos Gamarra.
But Chilavert and some in the Paraguayan FA are not so sure.
Enciso blotted his copybook when he declared himself unavailable for last August's qualifier away to Brazil.
Crucial to Brazil's chances, it was a strange match all round, featuring an illegal change of venue and some eccentric refereeing.
Enciso had a long spell in Brazilain football with the Internacional club.
He has a Brazilian agent, Gilmar Veloz, who is a close friend of the rival coach.
According to Chilavert, Veloz phoned Paraguay's then-coach Sergio
Markarian to tell him that Enciso had legal problems in Brazil, and would therefore have to miss the match.
When it was then revealed that no legal problems existed, Enciso had made some powerful enemies in the Paraguayan camp.
He has not played for his country since.
But leaving him out last year could be justified on purely footballing grounds.
He spent some time without a club, and the lack of activity took its toll.