diff --git a/milli/src/boost.rs b/milli/src/boost.rs
index 5571722bf..f90a68ee2 100644
--- a/milli/src/boost.rs
+++ b/milli/src/boost.rs
@@ -11,7 +11,7 @@ use crate::RankingRuleError;
 /// You must always cast it to a sort error or a criterion error.
 #[derive(Error, Debug)]
 pub enum BoostError {
-    #[error("Invalid syntax for the boost parameter: expected expression ending by `boost:`, found `{name}`.")]
+    #[error("Invalid syntax for the boost parameter: expected expression starting with `boost:`, found `{name}`.")]
     InvalidSyntax { name: String },
 }
 
@@ -26,12 +26,6 @@ impl From<BoostError> for RankingRuleError {
 #[derive(Debug, Serialize, Deserialize, Clone, PartialEq)]
 pub struct Boost(pub String);
 
-impl Boost {
-    pub fn filter(&self) -> &str {
-        &self.0
-    }
-}
-
 impl FromStr for Boost {
     type Err = BoostError;
 
@@ -42,103 +36,3 @@ impl FromStr for Boost {
         }
     }
 }
-
-#[cfg(test)]
-mod tests {
-    use big_s::S;
-    use BoostError::*;
-
-    use super::*;
-
-    #[test]
-    fn parse_asc_desc() {
-        let valid_req = [
-            ("truc:asc", Asc(Field(S("truc")))),
-            ("bidule:desc", Desc(Field(S("bidule")))),
-            ("a-b:desc", Desc(Field(S("a-b")))),
-            ("a:b:desc", Desc(Field(S("a:b")))),
-            ("a12:asc", Asc(Field(S("a12")))),
-            ("42:asc", Asc(Field(S("42")))),
-            ("_geoPoint(42, 59):asc", Asc(Geo([42., 59.]))),
-            ("_geoPoint(42.459, 59):desc", Desc(Geo([42.459, 59.]))),
-            ("_geoPoint(42, 59.895):desc", Desc(Geo([42., 59.895]))),
-            ("_geoPoint(42, 59.895):desc", Desc(Geo([42., 59.895]))),
-            ("_geoPoint(90.000000000, 180):desc", Desc(Geo([90., 180.]))),
-            ("_geoPoint(-90, -180.0000000000):asc", Asc(Geo([-90., -180.]))),
-            ("_geoPoint(42.0002, 59.895):desc", Desc(Geo([42.0002, 59.895]))),
-            ("_geoPoint(42., 59.):desc", Desc(Geo([42., 59.]))),
-            ("truc(12, 13):desc", Desc(Field(S("truc(12, 13)")))),
-        ];
-
-        for (req, expected) in valid_req {
-            let res = req.parse::<Boost>();
-            assert!(
-                res.is_ok(),
-                "Failed to parse `{}`, was expecting `{:?}` but instead got `{:?}`",
-                req,
-                expected,
-                res
-            );
-            assert_eq!(res.unwrap(), expected);
-        }
-
-        let invalid_req = [
-            ("truc:machin", InvalidSyntax { name: S("truc:machin") }),
-            ("truc:deesc", InvalidSyntax { name: S("truc:deesc") }),
-            ("truc:asc:deesc", InvalidSyntax { name: S("truc:asc:deesc") }),
-            ("42desc", InvalidSyntax { name: S("42desc") }),
-            ("_geoPoint:asc", ReservedKeyword { name: S("_geoPoint") }),
-            ("_geoDistance:asc", ReservedKeyword { name: S("_geoDistance") }),
-            ("_geoPoint(42.12 , 59.598)", InvalidSyntax { name: S("_geoPoint(42.12 , 59.598)") }),
-            (
-                "_geoPoint(42.12 , 59.598):deesc",
-                InvalidSyntax { name: S("_geoPoint(42.12 , 59.598):deesc") },
-            ),
-            (
-                "_geoPoint(42.12 , 59.598):machin",
-                InvalidSyntax { name: S("_geoPoint(42.12 , 59.598):machin") },
-            ),
-            (
-                "_geoPoint(42.12 , 59.598):asc:aasc",
-                InvalidSyntax { name: S("_geoPoint(42.12 , 59.598):asc:aasc") },
-            ),
-            (
-                "_geoPoint(42,12 , 59,598):desc",
-                ReservedKeyword { name: S("_geoPoint(42,12 , 59,598)") },
-            ),
-            ("_geoPoint(35, 85, 75):asc", ReservedKeyword { name: S("_geoPoint(35, 85, 75)") }),
-            ("_geoPoint(18):asc", ReservedKeyword { name: S("_geoPoint(18)") }),
-            ("_geoPoint(200, 200):asc", GeoError(BadGeoError::Lat(200.))),
-            ("_geoPoint(90.000001, 0):asc", GeoError(BadGeoError::Lat(90.000001))),
-            ("_geoPoint(0, -180.000001):desc", GeoError(BadGeoError::Lng(-180.000001))),
-            ("_geoPoint(159.256, 130):asc", GeoError(BadGeoError::Lat(159.256))),
-            ("_geoPoint(12, -2021):desc", GeoError(BadGeoError::Lng(-2021.))),
-            ("_geo(12, -2021):asc", ReservedKeyword { name: S("_geo(12, -2021)") }),
-            ("_geo(12, -2021):desc", ReservedKeyword { name: S("_geo(12, -2021)") }),
-            ("_geoDistance(12, -2021):asc", ReservedKeyword { name: S("_geoDistance(12, -2021)") }),
-            (
-                "_geoDistance(12, -2021):desc",
-                ReservedKeyword { name: S("_geoDistance(12, -2021)") },
-            ),
-        ];
-
-        for (req, expected_error) in invalid_req {
-            let res = req.parse::<Boost>();
-            assert!(
-                res.is_err(),
-                "Should no be able to parse `{}`, was expecting an error but instead got: `{:?}`",
-                req,
-                res,
-            );
-            let res = res.unwrap_err();
-            assert_eq!(
-                res.to_string(),
-                expected_error.to_string(),
-                "Bad error for input {}: got `{:?}` instead of `{:?}`",
-                req,
-                res,
-                expected_error
-            );
-        }
-    }
-}
diff --git a/milli/tests/search/mod.rs b/milli/tests/search/mod.rs
index 0ac26004c..2dd413ad7 100644
--- a/milli/tests/search/mod.rs
+++ b/milli/tests/search/mod.rs
@@ -147,6 +147,15 @@ pub fn expected_order(
                     new_groups
                         .extend(group.linear_group_by_key(|d| d.asc_desc_rank).map(Vec::from));
                 }
+                RankingRule::Boost(filter) => {
+                    // move the matching documents first, then the ones that don't match
+                    group.sort_by_key(|d| if execute_filter(filter, d).is_some() { 0 } else { 1 });
+                    new_groups.extend(
+                        group
+                            .linear_group_by_key(|d| execute_filter(filter, d).is_some())
+                            .map(Vec::from),
+                    );
+                }
                 RankingRule::Asc(_) | RankingRule::Desc(_) | RankingRule::Sort => {
                     new_groups.push(group.clone())
                 }