WordWeb Online

1. The quality of being hard to endure, uninviting or formidable
   - asperity, grimness, hardship, rigor [US], rigour [Brit, Cdn], severity, severeness, rigourousness [Brit, non-standard]
    
2. Excessive sternness
   "rigorousness of character";
   - severity, severeness, harshness, rigor [US], rigour [Brit, Cdn], rigourousness [Brit, non-standard], inclemency, hardness, stiffness

Type of: difficultness, difficulty, fix [informal], hole [informal], jam [informal], kettle of fish [informal], mess [informal], muddle [informal], pickle [informal], sternness, strictness