The decision was made unanimously at Wednesday's Ordinary Meeting of Council.
The Cobomba weed has been been found in Lake Benalla since the early ‘90s.
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The South American species is popular in home aquariums and it is believed it entered Victoria's waterways when home set-ups had been disposed of.
It is listed as a Weed of National Significance and is considered one of the worst in Australia because of its invasive nature, potential for spread, and its economical and environmental impacts.
The weed is well established in Lake Benalla and several previous draw-downs have so far been unsuccessful in eradicating it.
The most recent draw-down was in 2018.
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Several councillors, including Peter Davis, questioned if a winter draw-down would be possible.
Benalla Rural City environmental sustainability coordinator Larissa Montgomery said that option had been explored, but it would not be as effective.
The reason for that being that we have a wet winter forecast, which would affect the ability to draw-down the lake - and that the summer heat is an important factor in drying the weed out.
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