Alphabetize a string array without using Array.sort() or compareTo()?

I have an exercise in class where you take names from the user and output them alphabetically. I'm not allowed to use Array.sort() or compareTo(). I seem to have gotten it to work for the most part... Except for when I enter something like a aaa aa, it outputs it in the following order:

aaa
aa
a

I'd really like to be able to output it in this order instead:

a
aa
aaa

This is what I have so far:

public static void main(String args[]) throws IOException {

    BufferedReader key =
    new BufferedReader(new InputStreamReader(System.in));

    System.out.println("Alphabetizing names\n");

    System.out.println("Enter names separated by spaces:");
    StringTokenizer names1 = new StringTokenizer(key.readLine());

    int tokens = names1.countTokens();
    String[] names2 = new String[tokens];
    String y;

    for (int a = 0; a < tokens; a++) {

        names2[a] = names1.nextToken();

    }

    System.out.println("\nSorted names:");

    for (int a = 0; a < tokens; a++) {

        for (int b = a + 1; b < tokens; b++) {

            if(alphabetize(names2[a], names2[b])) {

                y = names2[a];
                names2[a] = names2[b];
                names2[b] = y;

            }

        }

    }

    for (int c = 0; c < tokens; c++) {

        System.out.println(names2[c]);

    }

}

static boolean alphabetize(String a, String b) {

    for(int c = 0; ; c++) {

        if((c == a.length()-1) && (c == b.length()-1)) {

            return false;

        }

        if(c == a.length()-1) {

            return true;

        }

        if(c == b.length()-1) {

            return false;

        }

        if((a.toLowerCase().charAt(c) - b.toLowerCase().charAt(c)) > 0) {

            return true;

        }

    }

}

Please help!! Thank you!