  Recently Badziag \emph{et al.} \cite{badziag} obtained a class of noisy
states whose teleportation fidelity can be enhanced by subjecting one of the
qubits to dissipative interaction with the environment via amplitude damping
channel (ADC). We show that such noisy states result while sharing the states
(| \Phi ^{\pm}> =\frac{1}{\sqrt{2}}(| 00> \pm | 11>)) across ADC. We also show
that under similar dissipative interactions different Bell states give rise to
noisy entangled states that are qualitatively very different from each other in
the sense, only the noisy entangled states constructed from the Bell states (|
\Phi ^{\pm}>) can \emph{}be made better sometimes by subjecting the unaffected
qubit to a dissipative interaction with the environment. Importantly if the
noisy state is non teleporting then it can always be made teleporting with this
prescription. We derive the most general restrictions on improvement of such
noisy states assuming that the damping parameters being different for both the
qubits. However this curious prescription does not work for the noisy entangled
states generated from (| \Psi ^{\pm}> =\frac{1}{\sqrt{2}}(| 01> \pm | 10>)).
This shows that an apriori knowledge of the noisy channel might be helpful to
decide which Bell state needs to be shared between Alice and Bob. \emph{}
