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Gillingham sank to the bottom of League 1 following a home defeat on Saturday.
The 1-0 loss to Bradford extended The Gills run without a win at the start of the season to 10 games in all competitions.
Bradford went ahead early on through their captain Gary Jones and it proved to be enough for the visitors.
Gills manager Martin Allen made two changes to his starting eleven, bringing Adebayo Akinfenwa into the team, to partner Cody McDonald upfront for the first time this season.
Charlie Lee also made an immediate return to the team, following a ban, with Danny Kedwell and Charlie Allen the men left out.
Bradford made a lively start to the game, with winger Kyel Reid helping the pull the Gills defence around. With eight minutes gone the visitors went ahead from a corner.
Jones, who took the flag-kick, was claiming the goal but a flick from Andrew Davies may have been vital to deceive Gills keeper Stuart Nelson. Bradford's Garry Thompson was also claiming it, but few at Priestfield cared who scored.
The Gills’ hopes of keeping their first clean sheet of the season had quickly disappeared.
Reid continued to run at the Gills defence and cause problems but the Gills had a number of chances in the first half. Lee shot an effort narrowly wide, Adam Barrett’s hooked effort was saved and the keeper also did well to get down and deny Myles Weston.
Bradford went into the break wondering how they hadn’t doubled the lead, however, as big striker James Hanson somehow headed wide, when a cross from the right found him free in space, just a couple of yards out.
Bradford made a bright start to the second half and had appeals early on for a penalty, when Reid went down in the box following a Leon Legge challenge. From the resulting corner Rory McArdle headed wide.
McDonald blazed a great chance over the bar with 53 minutes gone. Akinfenwa only half connected to an overhead kick, the ball fell at McDonald’s feet, but unfortunately the Gills number 10 couldn’t capitalise.
The Gills did a much better job of keeping Bradford’s dangermen quiet in the second half but chances were less forthcoming for the hosts as well. McDonald thought he had finally found a way through, after latching onto Danny Hollands’ throughball, but the linemsman’s flag was up as he took the ball past the keeper.
With Antonio German’s introduction for the last 15 minutes, the game opened up again, as the Gills went for broke with three forwards. Bradford immediately responded and twice Wells went close. His first chance was fired over and the second skimmed the bar.
The Gills put the pressure on in the latter stages, with a succession of corners, but were unable to find a way through. A good save from Nelson on 90 minutes denied Wells from doubling the lead.
Gillingham: Nelson, Martin, Harriman, Barrett, Legge, Hollands, Linganzi, Lee (Whelpdale 66mins), Weston (German 76mins), Akinfenwa (Kedwell 58mins), McDonald. Subs not used: Davies, Allen, Dack, Howard.
Bradford City: McLaughlin, Darby, Meredith, Davies, Reid (Yeates 79mins), Hanson, Thompson, Jones, Wells (Connell 90mins), McArdle, Doyle. Subs not used: Ravenhill, Oliver, Gray, Ripley, De Vita.