Consider:
---
enum E { A; }
---

This compiled&decompiled leads to:
---
  private E();
    descriptor: (Ljava/lang/String;I)V
    flags: ACC_PRIVATE
    Code:
      stack=3, locals=3, args_size=3
         0: aload_0       
         1: aload_1       
         2: iload_2       
         3: invokespecial #6                  // Method java/lang/Enum."<init>":(Ljava/lang/String;I)V
         6: return        
      LineNumberTable:
        line 1: 0
    Signature: #24                          // ()V
---

The Signature attribute is not mandatory in this case (as the constructor's parameters are not generic). Avoiding the attribute may provide smaller, cleaner classfiles, and so should be considered.