What Constitutes On Cover?

I have a number of envelope pieces with scott#017 Dept of Interior,
some have 3 stamps plus postmark but no full envelope.
Are those considered covers?

I think it's considered to be "on piece". At least that's how I would describe it.

on piece... so not the same price as on cover but more than a single soaked off?

Agreed. On cover would be representative of the stamp on the full envelope in which it was received, bearing all postal markings and are priced that way in the Scott Catalog. If there is only a piece, only a front, only a corner cut with the stamp and postmark, that is not valued as an item "on cover".

Is there a premium for such things? Possibly. However, in my opinion, unless the item is considered quite scarce or rare, my guess is that most collectors would not be interested in paying much of a premium for an "on piece" item if it can easily be obtained "on cover". In my mind, if it is not in a traditional "collectible state", it would not be very desirable on the secondary market (at least not at a premium over the stamp itself).

That doesn't necessarily mean it may not garner a small premium in value, but it would all have to come back to an agreement between what one is willing to sell it for and what a buyer is willing to pay, as there is no possible way all such items could ever be catalogued.

If the postmark is really nice, I would leave it on piece.

From the 2011 Scott Specialized:

"The Scott Catalogue value for a stamp on cover, as for a stamp off cover, is a retail value; that is, an amount you could expect to pay for that cover in the grade of Very Fine, as defined below. Folded letters, folded covers, envelopes, stationery entires and newspapers are valued as whole and complete, not as fronts of letter sheets or envelopes or as fragments of newspapers or circulars. Values given are for covers bearing stamps that are "tied on" by the cancellation..."