Short relatively deep tidal basins, which are connected to the open sea by a narrow strait, may exhibit either an amplified (resonant), or damped (choked) response to the tide at the entrance. Here particular attention is given to the lowest mode of response, which is the Helmholtz or pumping mode, for which the sea level within the basin executes a spatially uniform oscillation. When the basin's sidewalls slope, the restoring process of this oscillator is nonlinear. Possible consequences of this nonlinearity are that the basin may exhibit either long-lasting high-waters and short, peaked low-waters or long-term regular modulation of its tidal amplitude, or a chaotic modulation of its tidal amplitude, or ‘bent resonance horns’, implying that resonant and choked tidal responses may exist simultaneously for the same parameter regime. Related field observations will be discussed.