The net operating loss from the previous year would appear as "Other Income" on the current year tax return. If you had losses in the current year, they would also appear on the tax return, which could result in a loss larger than the NOL from the previous year to be carried over to the next year.
One NOL is the same as another, so I'm not sure why it would matter which one was applied to the current year first, since both of them will be a component of the current year net loss, which will then be carried over to the next year.
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