I am still in Fukuoka, and last month, my brother, his wife and their 7-year-old son (my nephew) also gathered at my mother's house on the occasion of my late father's sixth death anniversary. At that time, I was mainly indulging in the cute conversations with Tatsunori-kun, the nephew.
Ever wonder what to say in the place of "no, thank you" in Japanese? A textbook answer (particularly I often hear from Japanese learners in Pune) is, "いいえ、結構です (iie, kekkou desu,)" isn't it? However, I had long been feeling a sense of incongruity of the phrase as it sounds rather stronger than intended meaning and also is not very commonly used.
I learned the best answer from Tatsunori-kun, which is "大丈夫 (です) [Daijoubu (desu.)]"
According to a dictionary, the modern application of "Daijoubu" is to confirm or answer the opponent of the conversation whether it is necessary or not, possible or not, or approved or not. The examples in the dictionary are like "重そうですね、持ちましょうか (Shall I carry the load on your behalf?)," "いえ、大丈夫です (It's alright, thank you,)" "試着したいのですが大丈夫ですか ([in a boutique] May I try the cloth on me?)」「はい、大丈夫です (Yes, you may.)"
I believe I have been using "Daijoubu" without consciousness before learning from Tatsunori-kun, but thanks to him, now I am more confident in applying it on most occasions where I must politely refuse!