We address stationary patterns in exciton-polariton condensates supported by a narrow external pump beam, and we discover that even in the absence of trapping potentials, such condensates may support stable localized stationary dissipative solutions (quasicompactons), whose field decays faster than exponentially or even vanishes everywhere outside the pump spot. More general conditions lead to dissipative solitons which may display bistability. The bistability in exciton-polariton condensates, which manifests itself in the simultaneous existence of two stable and one unstable localized solitons with different amplitudes, widths, and exciton-photon fractions under the same physical conditions, strongly depends on the width of the pump beam and is found to disappear for sufficiently narrow pump beams

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