diff --git a/sphinx-docs/comparisons.md b/sphinx-docs/comparisons.md
new file mode 100644
index 0000000..38e2517
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+++ b/sphinx-docs/comparisons.md
@@ -0,0 +1,119 @@
+# Comparisons
+
+## Overview
+
+The `comparisons` configuration section defines constraints on the matching
+process. Unlike `comparison_features` and `feature_selections`, which define
+features for use with a machine-learning algorithm, `comparisons` define rules
+which directly filter the output `potential_matches` table. These rules often
+depend on some comparison features, and hlink always applies the rules after
+exploding and blocking in the matching task.
+
+As an example, suppose that your `comparisons` configuration section looks like
+the following.
+
+```
+[comparisons]
+comparison_type = "threshold"
+feature_name = "namefrst_jw"
+threshold = 0.79
+```
+
+This comparison defines a rule that depends on the `namefrst_jw` comparison
+feature. During matching, only pairs of records with `namefrst_jw` greater than
+or equal to 0.79 will be added to the potential matches table. Pairs of records
+which do not satisfy the comparison will not be potential matches.
+
+## Comparison Types
+
+Currently the only `comparison_type` supported for the `comparisons` section is
+`"threshold"`. This requires the `threshold` attribute, and by default, it
+restricts a comparison feature to be greater than or equal to the value given
+by `threshold`. The configuration section
+
+```
+[comparisons]
+comparison_type = "threshold"
+feature_name = "namelast_jw"
+threshold = 0.84
+```
+
+adds the condition `namelast_jw >= 0.84` to each record pair considered during
+matching. Only record pairs which satisfy this condition are marked as
+potential matches.
+
+Hlink also supports a `threshold_expr` attribute in `comparisons` for more
+flexibility. This attribute takes SQL syntax and replaces the `threshold`
+attribute described above. For example, to define the condition `flag < 0.5`,
+you could set `threshold_expr` like
+
+```
+[comparisons]
+comparison_type = "threshold"
+feature_name = "flag"
+threshold_expr = "< 0.5"
+```
+
+Note that there is now no need for the `threshold` attribute because the
+`threshold_expr` implicitly defines it.
+
+## Defining Multiple Comparisons
+
+In some cases, you may have multiple comparisons to make between record pairs.
+The `comparisons` section supports this in a flexible but somewhat verbose way.
+Suppose that you would like to combine two of the conditions used in the
+examples above, so that record pairs are potential matches only if `namefrst_jw >= 0.79`
+and `namelast_jw >= 0.84`. You could do this by setting the `operator`
+attribute to `"AND"` and then defining the `comp_a` (comparison A) and `comp_b`
+(comparison B) attributes.
+
+```
+[comparisons]
+operator = "AND"
+
+[comparisons.comp_a]
+comparison_type = "threshold"
+feature_name = "namefrst_jw"
+threshold = 0.79
+
+[comparisons.comp_b]
+comparison_type = "threshold"
+feature_name = "namelast_jw"
+threshold = 0.84
+```
+
+Both `comp_a` and `comp_b` are recursive, so they may have the same structure
+as the `comparisons` section itself. This means that you can add as many
+comparisons as you would like by recursively defining comparisons. `operator`
+may be either `"AND"` or `"OR"` and defines the logic for connecting the two
+sub-comparisons `comp_a` and `comp_b`. Defining more than two comparisons can
+get pretty ugly and verbose, so make sure to use care when defining nested
+comparisons. Here is an example of a section with three comparisons.
+
+```
+# This comparisons section defines 3 rules for potential matches.
+# They are that potential matches must either have
+# 1. flag < 0.5
+# OR
+# 2. namefrst_jw >= 0.79 AND 3. namelast_jw >= 0.84
+[comparisons]
+operator = "OR"
+
+[comparisons.comp_a]
+comparison_type = "threshold"
+feature_name = "flag"
+threshold_expr = "< 0.5"
+
+[comparisons.comp_b]
+operator = "AND"
+
+[comparisons.comp_b.comp_a]
+comparison_type = "threshold"
+feature_name = "namefrst_jw"
+threshold = 0.79
+
+[comparisons.comp_b.comp_b]
+comparison_type = "threshold"
+feature_name = "namelast_jw"
+threshold = 0.84
+```
diff --git a/sphinx-docs/index.rst b/sphinx-docs/index.rst
index efdb528..f2efb53 100644
--- a/sphinx-docs/index.rst
+++ b/sphinx-docs/index.rst
@@ -24,6 +24,7 @@ Configuration API
    :caption: Configuration API
 
    Column Mappings <column_mappings.md>
+   comparisons
    Comparison Types <comparison_types.md>
    Feature Selection <feature_selection_transforms.md>
    Pipeline Features <pipeline_features.md>