What Jesus considered great faith

Recently during my quiet time I came across the Canaanite woman in Mt. 15, 21 - 28 again. As you may remember, she approached Jesus because her daughter was desperately afflicted by a demon. Jesus insisted that he had only been sent to the Jews, and that it wasn't right to take the children's bread and throw it to the dogs. Undeterred, she humbled herself, comparing herself to a little dog in the household that is feeding on the crumbs. Jesus marveled at her great faith and granted her wish.

Why was her faith so great? First of all, she believed that just a tiny amount of Jesus' power would suffice - a crumb, "just a dab will do ya." Second, she wasn't afraid to humble herself. Far from bristling at Jesus' comparing her with a dog, she agreed with him and pleaded for mercy. Therefore she, the outsider who wasn't even supposed to have the good news preached to her at this time, received what she asked for.

A similar combination of deep humility, plus great faith that just a tiny amount of Jesus' power is sufficient, can be seen in two other Gospel characters - incidentally, both of them outsiders as well. There was the centurion, one of the hated Roman occupiers, coming to Jesus with the request to heal his servant. (Mt. 8:5-13) But he, too, humbled himself, calling himself not worthy to have Jesus visit him at home. Instead, he believed that a simple word would heal his servant.
Jesus commended his great faith and said it was greater than that of anyone in Israel (v. 10).

Finally, there was the woman with the blood flow. (Mk. 5, 25 - 34) She, too, was so humble that she didn't even dare approach Jesus directly but snuck up on him from behind. Although she was the only Jew among the three, she had been unclean all these years because of her illness, and technically she was contaminating the Rabbi. Like the others, she believed that just a touch was needed to heal her. She believed that she only needed to touch the hem of his garment to be healed. And it was so.

How much do I believe that "just a dab of his power will do me?"
And am I as humble in heart as those whom Jesus loved?