Ocean surface altimetry with GNSS reflectometry (GNSS-R) has the potential to improve the observation and retrieval of mesoscale ocean current flows by increasing the spatial density of ocean surface observations. The leading challenges in current GNSS-R altimetry investigations include precise delay retracking, correction of ionospheric effects, and spacecraft receiver positioning. Here, we present improved methods to account for these challenges. A reflection-model-based approach is presented for delay retracking that uses simulated delay-Doppler maps (DDMs) to retrieve the specular delay from measured DDMs. Global ionosphere maps are used to estimate the group delay effect along the direct and reflection paths. Precise orbit determination techniques are used to improve estimates of the receiving spacecraft position and reduce systematic intersatellite biases. We analyze altimetric height retrievals from two cases, strongly coherent or diffuse reflections. We study the residual systematic error signals with a focus on understanding the errors identified above. The strong coherent observations have narrow, symmetric delay waveforms and provide higher than average signal-to-noise ratio. The DDMs of diffuse observations, originate from relatively rough ocean surfaces and have the characteristic horse-shoe shape. Only measurements from the ocean and seas surrounding Indonesia are considered as this area provides a significant number of strongly coherent reflections. More than 50 000 single-point observations and week-long averaged results are presented to quantify the noise and systematic characteristics of the retrieved surface heights.