OK, I'm mystified by this.

1. Create simple Apex class

2. Override log filters in Force.com user interface to:

• Database = NONE
• Workflow = NONE
• Validation = NONE
• Callouts = NONE
• Apex Code = INFO
• Apex Profiling = NONE
• Visualforce = NONE
• System = NONE

3. Run Test on Class (also in Force.com UI: Setup | Develop |Apex Classes | <class> | Run Test)

RESULT:

• Although APEX Profiling log filter is NONE, I still get an APEX profile
• Although APEX Code = INFO, I still get Static variable listings - these are supposed to show only if Apex Code = FINE, FINER, FINEST
• Furthermore, the debug log header echoed by SFDC has no bearing on the override filters I specified. Instead, it shows: 

25.0 APEX_CODE,FINE;APEX_PROFILING,FINE;DB,INFO;VALIDATION,INFO;WORKFLOW,FINEST

• Yet, the actual Apex Code log filter is honored as only my System.debug statement at LoggingLevel.INFO is displayed whereas the line at LoggingLevel.DEBUG is not (as expected)

You might say, so what? But when you have big complex APEX classes and multiple triggers firing, and a lot of constants, the debug log fills up with all sorts of noise that gets in the way

By the way, here's the code:

public without sharing class MyClass { 
    public static final String MY_CONSTANT = 'My Constant';
    //    Constructor
    public MyClass() {
        

        System.debug(LoggingLevel.INFO,'should display on log filter INFO');
        System.debug(LoggingLevel.DEBUG,'should display on log filter DEBUG');
    }
    static testmethod void testMyClass () {
        MyClass myc = new MyClass();
    }
}

 and here's the debug log:

25.0 APEX_CODE,FINE;APEX_PROFILING,FINE;DB,INFO;VALIDATION,INFO;WORKFLOW,FINEST
12:46:46.443 (6443874000)|EXECUTION_STARTED
12:46:46.443 (6443924000)|CODE_UNIT_STARTED|[EXTERNAL]|01pM00000009AuA|MyClass.testMyClass
12:46:46.445 (6445382000)|USER_DEBUG|[7]|INFO|should display on log filter INFO
12:46:40.396 (6445485000)|CUMULATIVE_LIMIT_USAGE
12:46:40.396|LIMIT_USAGE_FOR_NS|(default)|
  Number of SOQL queries: 0 out of 100
  Number of query rows: 0 out of 50000
  Number of SOSL queries: 0 out of 20
  Number of DML statements: 0 out of 150
  Number of DML rows: 0 out of 10000
  Number of script statements: 3 out of 200000
  Maximum heap size: 0 out of 6000000
  Number of callouts: 0 out of 10
  Number of Email Invocations: 0 out of 10
  Number of fields describes: 0 out of 100
  Number of record type describes: 0 out of 100
  Number of child relationships describes: 0 out of 100
  Number of picklist describes: 0 out of 100
  Number of future calls: 0 out of 10

12:46:40.396|TOTAL_EMAIL_RECIPIENTS_QUEUED|0
12:46:40.396|STATIC_VARIABLE_LIST|
  String:_static_MY_CONSTANT:0
  double:MIN_NORMAL:0
  double:POSITIVE_INFINITY:0
  long:serialVersionUID:0
  Boolean:TRUE:0
  double:MIN_VALUE:0
  int:SIZE:0
  int[]:sizeTable:0
  char[]:DigitOnes:0
  char[]:DigitTens:0
  String:_sfdcAdditionalCodeLocations:0
  double:NaN:0
  double:NEGATIVE_INFINITY:0
  int:MIN_VALUE:0
  int:SIZE:0
  double:MAX_VALUE:0
  String:_sfdcSuppressedCodeLocations:0
  long:serialVersionUID:0
  int:MAX_EXPONENT:0
  int:MIN_EXPONENT:0
  Boolean:FALSE:0
  String:_sfdcSuppressedCodeLocations:0
  int:MAX_VALUE:0
  char[]:digits:0
  long:serialVersionUID:0

12:46:40.396|CUMULATIVE_LIMIT_USAGE_END

12:46:46.445 (6445636000)|CODE_UNIT_FINISHED|MyClass.testMyClass
12:46:46.445 (6445647000)|EXECUTION_FINISHED
12:46:41.398|CUMULATIVE_PROFILING_BEGIN
12:46:41.398|CUMULATIVE_PROFILING|No profiling information for SOQL operations
12:46:41.398|CUMULATIVE_PROFILING|No profiling information for SOSL operations
12:46:41.398|CUMULATIVE_PROFILING|No profiling information for DML operations
12:46:41.398|CUMULATIVE_PROFILING|method invocations|
External entry point: static testMethod void testMyClass(): executed 1 time in 1 ms
Class.MyClass.<init>: line 7, column 1: global public static void debug(APEX_OBJECT, ANY): executed 1 time in 0 ms
Class.MyClass.<init>: line 8, column 1: global public static void debug(APEX_OBJECT, ANY): executed 1 time in 0 ms
Class.MyClass.testMyClass: line 11, column 1: public MyClass(): executed 1 time in 0 ms

12:46:41.398|CUMULATIVE_PROFILING_END

 Thanks