This note seeks to evaluate the self-propulsion of a micro-organism, in a viscous fluid, by sending a helical wave down its flagellated tail. An explanation is provided to resolve the paradoxical phenomenon that a micro-organism can roll about its longitudinal axis without passing bending waves along its tail (Rothschild 1961, 1962; Bishop 1958; Gray 1962). The effort made by the organism in so doing is not torsion, but bending simultaneously in two mutually perpendicular planes. The mechanical model of the micro-organism adopted for the present study consists of a spherical head of radius
a
and a long cylindrical tail of cross-sectional radius
b
, along which a helical wave progresses distally. Under the equilibrium condition at a constant forward speed, both the net force and net torque acting on the organism are required to vanish, yielding two equations for the velocity of propulsion,
U
, and the induced angular velocity,
Ω
, of the organism. In order that this type of motion can be realized, it is necessary for the head of the organism to exceed a certain critical size, and some amount of body rotation is inevitable. In fact, there exists an optimum head-tail ratio
a/b
at which the propulsion velocity
U
reaches a maximum, holding the other physical parameters fixed. The power required for propulsion by means of helical waves is determined, based on which a hydromechanical efficiency
η
is defined. When the head-tail ratio
a/b
assumes its optimum value and when
b
is very small compared with the wavelength
λ, η ≃ Ω/ω
approximately (
Ω
being the induced angular velocity of the head,
ω
the circular frequency of the helical wave). This
η
reaches a maximum at
kh
≃ 0.9 (
k
being the wavenumber 2π/
λ
, and
h
the amplitude of the helical wave). In the neighbourhood of
kh
= 0.9, the optimum head-tail ratio varies in the range 15 <
a/b
< 40, the propulsion velocity in 0.08 <
U/c
< 0.2 (
c
=
ω/k
being the wave phase velocity), and the efficiency in 0.14 <
η
< 0.24, as
kb
varies over 0.03 <
kb
< 0.2, a range of practical interest. Furthermore, a comparison between the advantageous features of planar and helical waves, relative to each other, is made in terms of their propulsive velocities and power consumptions.