Possible Clues:

• Drink for a drifter? It'll have no great effect (1,4,2,3,5)
• Indian descent possibly of little consequence
• Insignificant amount (notice letters 5 to 8 in this answer)
• Piano C note heard to be discordant, not enough to matter? (1,4,2,3,5)
• Tiny part of the whole
• Certainly no effect of global warming is very little (1,4,2,3,5)
• Insignificant part of the whole Mariana Trench? (1,4,2,3,5)
• A fall in sea level is something insignificant (1,4,2,3,5)
• Hardly any at low tide? (1,4,2,3,5)
• The end result of walking the plank doesn't amount to much (1,4,2,3,5)