Limiting SDL output in full screen mode to window's bounds

I am developing a GTK application with a drawable in which a mediaplayer’s
video output will be displayed. I use the environment variable SDL_WINDOWID
to give the SDL to use the window of the drawing area.

       long sdl_xwid;
       sdl_xwid = GDK_DRAWABLE_XID (screen->window); //where screen is a

Gtk_Drawable widget

        char SDL_windowhack[32];
        sprintf (SDL_windowhack, "SDL_WINDOWID=%ld", sdl_xwid);
        putenv (SDL_windowhack);

The display of video on drawing the area is fine in normal screen mode. When
i change to full screen mode, only a part of the zoomed video is seen on the
drawing area. The window has to be resized to view the complete screen. How
do i limit the full screen video display to within the bounds of the
drawing area (which is 320 X 240 pixels)?
Is there any SDL environment variable available for this purpose?