In two-step population screening for colorectal cancer (CRC), a simple non-invasive test, commonly a fecal immunochemical test for hemoglobin (FIT), is first undertaken to predict, based on the fecal hemoglobin concentration (f-Hb), who is more likely to have colorectal neoplasia and needs colonoscopy. To evaluate the importance of being able to adjust the f-Hb threshold that triggers follow-up colonoscopy (the "positivity threshold"), we evaluated the predictive value of f-Hb for colorectal neoplasia and its implications for the configuration of new non-invasive tests. A literature review was conducted on the use of quantitative FIT to select the positivity threshold, followed by using f-Hb from a large population to model how adjusting the positivity threshold enabled achievement of the desired program outcomes in a feasible manner. The literature review and the modeling found that while the f-Hb positivity threshold is predictive for colorectal neoplasia across a wide range of f-Hb, there is a complex relationship between program outcomes and f-Hb. The threshold determines not just clinical accuracy (including true- and false-positive results for CRC and/or advanced precursor lesions), but also the colonoscopy workload. A lower f-Hb threshold is associated with a higher sensitivity for neoplasia but a lower specificity and a heavier load of follow-up colonoscopies. Consequently, the threshold determines a program's impact on population CRC mortality and incidence, but also its feasibility and cost-effectiveness within a health-care system. We are entering a new era of non-invasive screening tests, where multiple biomarkers found in biological samples such as blood as well as feces, are being developed and evaluated. These typically specify a non-transparent algorithm, developed with machine learning, to provide a predictive dichotomous positive/negative result with a fixed associated clinical accuracy and colonoscopy workload. This will restrict use of new tests in jurisdictions where the accuracy and workload implications do not match the desired screening program outcomes. However, similar to flexible FIT positivity thresholds, it would be ideal if new tests also provide capacity for screening program providers to select the positivity threshold that delivers their desired screening outcomes in a feasible manner. How marketing, distribution and reimbursement of non-invasive tests are approved, funded and implemented varies widely across jurisdictions and must be taken into account.