A needle apparatus and method of manufacturing the same arc disclosed. The needle apparatus includes a tubular needle component having a handling end including a needle hub and an insertion end including a pointed portion configured for piercing tissue of a patient. The needle apparatus also includes a cover forming a sleeve surrounding the tubular needle component. The cover extends along an outer surface of the tubular needle component such that the insertion tip of the needle remains uncovered. The cover includes a tapered end coupled to the tubular needle component adjacent to the insertion tip of the needle. The tapered end of the cover has a taper angle of 5-20 degrees with respect to the outer surface of the tubular needle component.