There again, when Bristol came out at home to Leicester on 28 January their captain was given not only the biggest match of the round but also a direct confrontation with Neil Back, the only genuine open-side flanker in the England squad who will spend the new year on Lanzarote.
Most sensible people would rather see in 1995 at home than on a training trip to the Canaries. But not Eves, for whom the cup tie will be his second game against Back in a month. Next Tuesday, he will be one of three Bristol forwards - the others are thesecond-row pair, Simon Shaw and Andy Blackmore - in the Barbarians team fulfilling Welford Road's Christmas tradition.
Even Eves is beginning to wonder whether it will make any difference, the more so as Back - another of the smaller but faster back-row genre - has himself had inordinate difficulty persuading England selectors of his international worth. "I can't do any more," Eves said yesterday.
He could scarcely be expected to do any more than score three tries, as he did against Nottingham in the fourth round. "Everyone tells me I'm playing well, but there's obviously some reason they're not picking me. It's frustrating but that only makes me battle all the harder."
Eves would have preferred to avoid Leicester at this stage but Bristol have a formidable home record against the Tigers, having won the last three matches including last month's by 31-22 which severely dented Leicester's hopes of keeping up with Bath.
Talking of which, the eight-times cup-winners will continue their defence - 11 years to the day since their ascendancy began with a 17-0 win over Headingley - at Orrell in the only other all-First Division tie.
Harlequins, who with Bath, Bristol and Leicester are the only surviving cup-winners after the dispatch of five in the fourth round, will play at London Irish. The coincidence that Quins keep being drawn against clubs from whom they have acquired players was clearly made in heaven.
In this post-relegation season, the Exiles have kindly supplied Quins with an Ireland full-back, Jim Staples, and England A flanker, Rory Jenkins. Last Saturday, Quins edged out Saracens, another of their suppliers.
Lydney of the Fifth Division, the lowliest of the last 16, are blessed with a home tie, the Forest of Dean being a place where Wakefield would fear to tread if they had not already impressed Forest folk by knocking out the local senior club, Gloucester.
Aspatria, of the Fourth, have the longest journey the draw could possible have given them, from Cumbria to Exeter, of the Third, with the other Third Division survivors, Richmond, ill-served by a visit to Northampton of the First.
PILKINGTON CUP Fifth round: Bristol v Leicester; Waterloo v Wasps; Northampton v Richmond; Sale v Fylde; Orrell v Bath; London Irish v Harlequins; Lydney v Wakefield; Exeter v Aspatria. (To be played 28 January).