The Black Country Mail Extra and the Wolverhampton Adnews will no longer be published. Trinity Mirror will concentrate on the Walsall Observer in the area.
Trinity Mirror said that although the Daventry Post would close, the Warwickshire and Leamington Times would continue to cover the region.
In Ashby, the Ashby Herald will close and the Ashby Trader and Echo will continue to be published.
A spokesman said the distribution models of the remaining titles would not change as a result of the closures.
Trinity Mirror said it hoped redundancies would be avoided due to "redeployment" of staff to "other titles and projects".
Trinity Mirror has closed 32 weekly titles since the beginning of 2008.
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