Lightroom CC 2015.7 won't import small .tif scans

We are scanning old photos into lightroom. Sometimes the photos have descriptions written on the back, and are small in size, often under 40k, or even smaller.

When we import these, we get an error message, and they are not imported.  Error message says the file appears to be unsupported or damaged. (1)

Is there a size restriction for importing into Lightroom?

If so, can it be adjusted?

If not, can we adjust the settings that we scan with to make this scans larger in size?

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