For Chanukha Shulchan Aruch (תרעא:ו) writes:
...מניחו למעלה משלשה טפחים
To which the Mishneh Berura writes:
דכל למטה משלשה כאלו הניח בקרקע ואין ניכר שבעל הבית הניחו שם
"For anything below three tefachim its as if one placed it on the ground and it is not noticeable that the house-owner placed it there"
Is the three tefachim counted from the flame itself or from the base of the chanukiyah? If it is from the base then the flame could much higher than is acceptable (and no 'eye would notice it'). If it is from the flame then one could put your chanukiyah on the floor directly, as long as the flame is higher than 3 tefachim.
And finally, if the flame is the defining height would it need to be above 3 tefachim for the duration of the 30mins that the candle needs to be lit (i.e. as the flame burns the candle gets shorter) or as long as it starts above 3 tefachim then it's ok?