More Letter Boxes

In each puzzle below, place the pieces into a 3x3 grid. The pieces will overlap, but when completed, there will be exactly one number and one letter in each box. 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
 
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
|   |   |   |
+---+---+---+
Puzzle 1: 
+---+---+  +---+  +---+---+  +---+---+
|   | A |  | B |  | 5 |   |  |   | 6 |
+---+---+  +---+  +---+---+  +---+---+
|   |      |   |      |   |  |   |
+---+      +---+---+  +---+  +---+
| 1 |      |   | 2 |  | E |  | F +
+---+      +---+---+  +---+  +---+

+---+          +---+---+  +---+---+
| D |          |   | C |  |   | 7 |
+---+---+---+  +---+---+  +---+---+
|   |   | 4 |  | 3 |      | G |
+---+---+---+  +---+      +---+

+---+---+---+  +---+---+  +---+
| 8 |   | H |  | I |   |  | 9 |
+---+---+---+  +---+---+  +---+

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Puzzle 1b:

Repeat puzzle 1 with the G-7 piece replaced by: 
+---+---+---+
|   |   | 7 |
+---+---+---+
+ G +
+---+

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Puzzle 2: 
  +---+---+---+         +---+  +---+
  | A |   |   |  +---+  | 5 |  | F |
  +---+---+---+  | B |  +---+  +---+
+---+---+ | 1 |  +---+  |   |  |   |
|   | 4 | +---+  |   |  +---+  +---+
+---+---+    +---+---+  | E |  | 6 |
|   |  +---+ | 2 |   |  +---+  +---+
+---+  | 3 | +---+---+    +---+  +---+
| D |  +---+---+---+      | G |  | 8 |
+---+  |   |   | C |  +---+---+  +---+
       +---+---+---+  | 7 |   |  | H |
  +---+---+  +---+    +---+---+  +---+
  |   | I |  | 9 |
  +---+---+  +---+

Source: Original.

Solutions were received from Jozef Hanenberg, Sudipta Das, Philippe Fondanaiche, Claudio Baiocchi, and Adrian Atanasiu. Here is a summary of the solutions. 
1) 
      +-----+-----+-----+
      | D 9 | B 5 | A 6 |
      +-----+-----+-----+
      | I 8 | C 7 | H 4 |
      +-----+-----+-----+
      | G 3 | F 1 | E 2 |
      +-----+-----+-----+
 
1 b ) 
      +-----+-----+-----+
      | B 9 | A 5 | C 6 |
      +-----+-----+-----+
      | D 8 | I 3 | H 7 |
      +-----+-----+-----+
      | G 1 | F 2 | E 4 |
      +-----+-----+-----+
 
2) 
      +-----+-----+-----+
      | F 3 | G 4 | B 5 |
      +-----+-----+-----+
      | A 7 | I 8 | C 9 |
      +-----+-----+-----+
      | D 6 | H 2 | E 1 |
      +-----+-----+-----+
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