I often work with strips that are less than 1 inch many are 3/4 inch. Heavy starch is my best way of dealing with cutting and sewing these skinny strips and maintaining accruacy. I buy the concentrate and use it full strenght prior to cutting when working with the really small diminesions. Do use the sand paper dots as mentioned in a earlier post to keep the ruler from sliding/slipping.
Just one note : when heavily starching fabrics let the starch completly saturate into the fabric... and if at all possible for the best results let the starch dry prior to ironing. I starch and the press and cut the next day.