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Player-boss James Rogers insists Hythe are still not clear of the relegation places just yet.
An 88th-minute winner from Jack Mayhew earned the Cannons maximum points as they beat Chichester 2-1 in Isthmian South East at Reachfields on Saturday.
Hythe are now unbeaten in three matches and seven points clear of third-bottom Sevenoaks, who occupy a potential relegation play-off spot.
But Rogers’ side have the joint-worst goal difference in the league and their manager isn’t getting carried away.
“I’m still looking over my shoulder,” Rogers conceded.
“We are still only seven points away from the bottom three, and you could say it’s six due to our poor goal difference. I think it’s still from us right down to the bottom (who is going to finish in the bottom three places).
“We seem to be doing okay at the moment, but I still have my eye on how clubs are getting on below us if I’m honest.
“We are on 30 points. I think we are looking at another three or four wins to definitely make sure we are absolutely safe.
“We have lost one in the last five now in the league. We are starting to pick up points and our performances are getting the results we deserve, which is the main thing.”
On-loan Tonbridge midfielder Luca Woodhouse opened the scoring against Chichester, before substitute Mayhew struck the late winner.
Rogers revealed: “We had to make a change to bring off Jacob Gilbert. He got a kick on his nose.
“The original change was to put Jack at right-back but we changed our mind and put him into midfield - and it’s lucky we did, really!
“It was his first game back from injury in four weeks, so it was nice to see him get the winning goal.”
Teenager Woodhouse continues to impress as well.
Rogers enthused: “Obviously, I have got Macca (Angels’ manager Steve McKimm) and Tom Parkinson (Academy manager) to thank at Tonbridge for that.
“He was in and around their first-team and in their Academy as well. He is highly thought of there, and I can see why. He has that little bit of quality.
“I think he is 17 but he is going to be a hell of a player if he continues on the way he is.”
Hythe will be without midfielder Alex Brown, who serves the second of a two-match ban for their trip to Burgess Hill this Saturday, but experienced defender Scott Doe should be back.
Rogers said: “When we played them at our place, we were not in a great place. We had a lot of injuries and a lot of young kids in for that one. They beat us 5-1 and they were well worth their win, to be fair.
“I was watching that game from the touchline. They are a good side but I’m quietly confident.
“We have given all the top sides in this league a run for their money, other than Hastings - the likes of Herne Bay and Ramsgate.
"We will not go to Burgess Hill and sit back. If we can get three points, it’s massive for us.”
Rogers confirmed midfielder Charlie Webster will be out for the rest of the season with a knee injury.
The Cannons will play either Corinthian or Ashford in the Kent Senior Cup quarter-final. They face each other on Tuesday.