FARMS around Settle and Grassington have been moved out of the infected area for foot and mouth disease.
The Ministry of Agriculture, Fisheries and Food has agreed to reduce the area where strict restrictions apply.
Exclusion areas still remain north of Horton-in-Ribblesdale and Kettlewell, west of Bentham, and to the east of Cross Hills.
North Yorkshire County Council also announced this week that a limited number of rights of way in Craven could be reopened.
But it stressed the approach would still be cautious, with the main priority to contain and eradicate the disease.
A council spokesman added: "Severe hardship is being caused to communities, and in particular the tourism industry, which now needs to be addressed in situations where there is little or no risk."
Rachel Mann, chief executive of Craven District Council and co-ordinator of The Craven Foot and Mouth Task Force, welcomed the news.
She said: "The Task Force will now look very carefully at what rights of way in the district can be opened without risking our disease free status.
"We will ensure that the views of the whole community are heard when considering any such openings, which could well pave the way for some limited openings in time for the May Day holiday.
"In the meantime we would continue to urge local people, as well as visitors, to respect the current restrictions in an effort to prevent the spread of the disease into the district."
The Task Force has also renewed its call to businesses in Craven, experiencing hardship because of the crisis to contact Craven District Council and register for business rate relief.
District councillors confirmed on Tuesday that rate relief should be offered to businesses facing serious financial hardship, but felt the funding should come from central Government. At the moment any shortfall will have to be met by the council.
Head of finance Vince Green said the financial impact on a small authority like Craven was extremely significant.
Coun David Crawford said he was prepared to face the consequences, even if that meant going to jail, for the council to withhold the money it had to pay out in rate relief, from the money it forwarded to central Government.
He said: "If we meet these costs, it's the local taxpayer who is subsidising the business rate."
Coun John Binns added: "Some businesses have been affected so badly that people could be made redundant and lose their jobs and those same people could find themselves giving this money out through their council tax when they are actually redundant!"
Coun Philip Barrett said it would be impossible for the district council to sustain this level of support for an indefinite period.
Councillors agreed to continue lobbying Government to give better financial support to smaller councils.
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