Is there a version of JavaScript’s String.indexOf() that allows for regular expressions?

In javascript, is there an equivalent of String.indexOf() that takes a regular expression instead of a string for the first first parameter while still allowing a second parameter ?

I need to do something like

str.indexOf(/[abc]/ , i);

and

str.lastIndexOf(/[abc]/ , i);

While String.search() takes a regexp as a parameter it does not allow me to specify a second argument!

Edit:
This turned out to be harder than I originally thought so I wrote a small test function to test all the provided solutions… it assumes regexIndexOf and regexLastIndexOf have been added to the String object.

function test (str) {
    var i = str.length +2;
    while (i--) {
        if (str.indexOf('a',i) != str.regexIndexOf(/a/,i)) 
            alert (['failed regexIndexOf ' , str,i , str.indexOf('a',i) , str.regexIndexOf(/a/,i)]) ;
        if (str.lastIndexOf('a',i) != str.regexLastIndexOf(/a/,i) ) 
            alert (['failed regexLastIndexOf ' , str,i,str.lastIndexOf('a',i) , str.regexLastIndexOf(/a/,i)]) ;
    }
}

and I am testing as follow to make sure that at least for one character regexp, the result is the same as if we used indexOf

//Look for the a among the xes
test(‘xxx’);
test(‘axx’);
test(‘xax’);
test(‘xxa’);
test(‘axa’);
test(‘xaa’);
test(‘aax’);
test(‘aaa’);