This is a 3 dimensional crossword.

Each small square grid is one layer of a 4x4x4 cubic grid. The directions Across and Down are within each layer, while the 'Through' direction goes from a cell in one layer to the corresponding cell in the next layer. To illustrate, the spot for 6-Through has been highlighted.

This particular grid has all 4-letter spots, and each live cell is in exactly 2 spots. So within each layer, those eight letters that are not intersections of Across and Down spots are cross-checked by Through spots.

This is quite a small puzzle, by way of an introduction to 3D grids. To set a 3D puzzle with about the same number of cells as a regular 15x15 grid (225 cells), I would use a 6x6x6 grid (216 cells).

1. 2. 3. 4.  
5. g 6. g
7. 8.  9.
10. g 11. g
 
g 12. g 13.
14.    
g   g  
15.    
 
16.  17.  
  g   g
18.    
  g   g
 
g 19. g 20.
21.    
g   g  
22.    

ACROSS

1,7. A lover, a note within, succulent

14. Entering part of main tour

15. Without a circle first, oval is nothing

16. A Joplin piece, plus a Shankar piece

18. Footwear with no time for mass disapproval

21. Thank me for break

22. Are educators offering saxaphone help?

DOWN

1. Aussie PM

3. Rowers glide poorly

12. Two preps in one

13. Look away, boss!

16. Steal Eastern garment

17. Crook joker

19. Name bad hair

20. Necessity born before Penny

THROUGH

2.   DIRT
4.   DASH
5.   BASH
6.   UNIT
8.   TIE?
9.   BUM!
10.  DONE
11.  TRIG

And no, I didn't accidentally leave the answers in ... this time!