diff --git a/Cargo.lock b/Cargo.lock
index bacbf939786..e1159c71201 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -2722,6 +2722,7 @@ dependencies = [
  "acvm",
  "async-lsp",
  "codespan-lsp",
+ "convert_case 0.6.0",
  "fm",
  "fxhash",
  "lsp-types 0.94.1",
diff --git a/tooling/lsp/Cargo.toml b/tooling/lsp/Cargo.toml
index c5203478f5a..353a6ade904 100644
--- a/tooling/lsp/Cargo.toml
+++ b/tooling/lsp/Cargo.toml
@@ -33,6 +33,7 @@ thiserror.workspace = true
 fm.workspace = true
 rayon = "1.8.0"
 fxhash.workspace = true
+convert_case = "0.6.0"
 
 [target.'cfg(all(target_arch = "wasm32", not(target_os = "wasi")))'.dependencies]
 wasm-bindgen.workspace = true
diff --git a/tooling/lsp/src/requests/completion.rs b/tooling/lsp/src/requests/completion.rs
index ad0cf0c5b9b..95ed49ac2f1 100644
--- a/tooling/lsp/src/requests/completion.rs
+++ b/tooling/lsp/src/requests/completion.rs
@@ -8,6 +8,7 @@ use completion_items::{
     crate_completion_item, field_completion_item, simple_completion_item,
     struct_field_completion_item,
 };
+use convert_case::{Case, Casing};
 use fm::{FileId, FileMap, PathString};
 use kinds::{FunctionCompletionKind, FunctionKind, ModuleCompletionKind, RequestedItems};
 use lsp_types::{CompletionItem, CompletionItemKind, CompletionParams, CompletionResponse};
@@ -563,7 +564,7 @@ impl<'a> NodeFinder<'a> {
             let location = Location::new(member_access_expression.lhs.span, self.file);
             if let Some(typ) = self.interner.type_at_location(location) {
                 let typ = typ.follow_bindings();
-                let prefix = ident.to_string();
+                let prefix = ident.to_string().to_case(Case::Snake);
                 self.complete_type_fields_and_methods(&typ, &prefix);
                 return;
             }
@@ -679,6 +680,8 @@ impl<'a> NodeFinder<'a> {
             at_root = idents.is_empty();
         }
 
+        let prefix = prefix.to_case(Case::Snake);
+
         let is_single_segment = !after_colons && idents.is_empty() && path.kind == PathKind::Plain;
         let module_id;
 
@@ -841,11 +844,11 @@ impl<'a> NodeFinder<'a> {
             segments.push(ident.clone());
 
             if let Some(module_id) = self.resolve_module(segments) {
-                let prefix = String::new();
+                let prefix = "";
                 let at_root = false;
                 self.complete_in_module(
                     module_id,
-                    &prefix,
+                    prefix,
                     path_kind,
                     at_root,
                     module_completion_kind,
@@ -855,7 +858,7 @@ impl<'a> NodeFinder<'a> {
             };
         } else {
             // We are right after the last segment
-            let prefix = ident.to_string();
+            let prefix = ident.to_string().to_case(Case::Snake);
             if segments.is_empty() {
                 let at_root = true;
                 self.complete_in_module(
@@ -1155,8 +1158,41 @@ impl<'a> NodeFinder<'a> {
     }
 }
 
+/// Returns true if name matches a prefix written in code.
+/// `prefix` must already be in snake case.
+/// This method splits both name and prefix by underscore,
+/// then checks that every part of name starts with a part of
+/// prefix, in order.
+///
+/// For example:
+///
+/// // "merk" and "ro" match "merkle" and "root" and are in order
+/// name_matches("compute_merkle_root", "merk_ro") == true
+///
+/// // "ro" matches "root", but "merkle" comes before it, so no match
+/// name_matches("compute_merkle_root", "ro_mer") == false
+///
+/// // neither "compute" nor "merkle" nor "root" start with "oot"
+/// name_matches("compute_merkle_root", "oot") == false
 fn name_matches(name: &str, prefix: &str) -> bool {
-    name.starts_with(prefix)
+    let name = name.to_case(Case::Snake);
+    let name_parts: Vec<&str> = name.split('_').collect();
+
+    let mut last_index: i32 = -1;
+    for prefix_part in prefix.split('_') {
+        if let Some(name_part_index) =
+            name_parts.iter().position(|name_part| name_part.starts_with(prefix_part))
+        {
+            if last_index >= name_part_index as i32 {
+                return false;
+            }
+            last_index = name_part_index as i32;
+        } else {
+            return false;
+        }
+    }
+
+    true
 }
 
 fn module_def_id_from_reference_id(reference_id: ReferenceId) -> Option<ModuleDefId> {
@@ -1172,3 +1208,19 @@ fn module_def_id_from_reference_id(reference_id: ReferenceId) -> Option<ModuleDe
         | ReferenceId::Reference(_, _) => None,
     }
 }
+
+#[cfg(test)]
+mod completion_name_matches_tests {
+    use crate::requests::completion::name_matches;
+
+    #[test]
+    fn test_name_matches() {
+        assert!(name_matches("foo", "foo"));
+        assert!(name_matches("foo_bar", "bar"));
+        assert!(name_matches("FooBar", "foo"));
+        assert!(name_matches("FooBar", "bar"));
+        assert!(name_matches("FooBar", "foo_bar"));
+
+        assert!(!name_matches("foo_bar", "o_b"));
+    }
+}
diff --git a/tooling/lsp/src/requests/completion/completion_items.rs b/tooling/lsp/src/requests/completion/completion_items.rs
index 70afc43fe55..d4190f5241c 100644
--- a/tooling/lsp/src/requests/completion/completion_items.rs
+++ b/tooling/lsp/src/requests/completion/completion_items.rs
@@ -9,7 +9,10 @@ use noirc_frontend::{
 };
 
 use super::{
-    sort_text::{default_sort_text, new_sort_text, operator_sort_text, self_mismatch_sort_text},
+    sort_text::{
+        crate_or_module_sort_text, default_sort_text, new_sort_text, operator_sort_text,
+        self_mismatch_sort_text,
+    },
     FunctionCompletionKind, FunctionKind, NodeFinder, RequestedItems,
 };
 
@@ -246,11 +249,17 @@ impl<'a> NodeFinder<'a> {
 }
 
 pub(super) fn module_completion_item(name: impl Into<String>) -> CompletionItem {
-    simple_completion_item(name, CompletionItemKind::MODULE, None)
+    completion_item_with_sort_text(
+        simple_completion_item(name, CompletionItemKind::MODULE, None),
+        crate_or_module_sort_text(),
+    )
 }
 
 pub(super) fn crate_completion_item(name: impl Into<String>) -> CompletionItem {
-    simple_completion_item(name, CompletionItemKind::MODULE, None)
+    completion_item_with_sort_text(
+        simple_completion_item(name, CompletionItemKind::MODULE, None),
+        crate_or_module_sort_text(),
+    )
 }
 
 fn func_meta_type_to_string(func_meta: &FuncMeta, has_self_type: bool) -> String {
diff --git a/tooling/lsp/src/requests/completion/sort_text.rs b/tooling/lsp/src/requests/completion/sort_text.rs
index a1dd0ba5e94..9bdc603660f 100644
--- a/tooling/lsp/src/requests/completion/sort_text.rs
+++ b/tooling/lsp/src/requests/completion/sort_text.rs
@@ -1,33 +1,39 @@
 /// Sort text for "new" methods: we want these to show up before anything else,
 /// if we are completing at something like `Foo::`
 pub(super) fn new_sort_text() -> String {
-    "3".to_string()
+    "a".to_string()
 }
 
 /// This is the default sort text.
 pub(super) fn default_sort_text() -> String {
-    "5".to_string()
+    "b".to_string()
+}
+
+/// We want crates and modules to show up after other things (for example
+/// local variables, functions or types)
+pub(super) fn crate_or_module_sort_text() -> String {
+    "c".to_string()
 }
 
 /// Sort text for auto-import items. We want these to show up after local definitions.
 pub(super) fn auto_import_sort_text() -> String {
-    "6".to_string()
+    "d".to_string()
 }
 
 /// When completing something like `Foo::`, we want to show methods that take
 /// self after the other ones.
 pub(super) fn self_mismatch_sort_text() -> String {
-    "7".to_string()
+    "e".to_string()
 }
 
 /// We want to show operator methods last.
 pub(super) fn operator_sort_text() -> String {
-    "8".to_string()
+    "f".to_string()
 }
 
 /// If a name begins with underscore it's likely something that's meant to
 /// be private (but visibility doesn't exist everywhere yet, so for now
 /// we assume that)
 pub(super) fn underscore_sort_text() -> String {
-    "9".to_string()
+    "g".to_string()
 }
diff --git a/tooling/lsp/src/requests/completion/tests.rs b/tooling/lsp/src/requests/completion/tests.rs
index aa91ef0c279..f45988834b4 100644
--- a/tooling/lsp/src/requests/completion/tests.rs
+++ b/tooling/lsp/src/requests/completion/tests.rs
@@ -356,14 +356,14 @@ mod completion_tests {
     async fn test_complete_path_after_colons_and_letter_shows_submodule() {
         let src = r#"
           mod foo {
-            mod bar {}
+            mod qux {}
           }
 
           fn main() {
-            foo::b>|<
+            foo::q>|<
           }
         "#;
-        assert_completion(src, vec![module_completion_item("bar")]).await;
+        assert_completion(src, vec![module_completion_item("qux")]).await;
     }
 
     #[test]
@@ -494,7 +494,7 @@ mod completion_tests {
 
           impl SomeStruct {
             fn foo() {
-                S>|<
+                So>|<
             }
           }
         "#;
@@ -517,7 +517,7 @@ mod completion_tests {
 
           impl Trait for SomeStruct {
             fn foo() {
-                S>|<
+                So>|<
             }
           }
         "#;
@@ -537,7 +537,7 @@ mod completion_tests {
         let src = r#"
           fn main() {
             for index in 0..10 {
-                i>|<
+                ind>|<
             }
           }
         "#;
@@ -558,13 +558,13 @@ mod completion_tests {
           fn lambda(f: fn(i32)) { }
 
           fn main() {
-            lambda(|var| v>|<)
+            lambda(|lambda_var| lambda_v>|<)
           }
         "#;
         assert_completion_excluding_auto_import(
             src,
             vec![simple_completion_item(
-                "var",
+                "lambda_var",
                 CompletionItemKind::VARIABLE,
                 Some("_".to_string()),
             )],
@@ -733,16 +733,19 @@ mod completion_tests {
         let src = r#"
             fn foo(x: i>|<) {}
         "#;
-        assert_completion(
-            src,
+
+        let items = get_completions(src).await;
+        let items = items.into_iter().filter(|item| item.label.starts_with('i')).collect();
+
+        assert_items_match(
+            items,
             vec![
                 simple_completion_item("i8", CompletionItemKind::STRUCT, Some("i8".to_string())),
                 simple_completion_item("i16", CompletionItemKind::STRUCT, Some("i16".to_string())),
                 simple_completion_item("i32", CompletionItemKind::STRUCT, Some("i32".to_string())),
                 simple_completion_item("i64", CompletionItemKind::STRUCT, Some("i64".to_string())),
             ],
-        )
-        .await;
+        );
     }
 
     #[test]
@@ -895,7 +898,7 @@ mod completion_tests {
     async fn test_suggest_struct_type_parameter() {
         let src = r#"
             struct Foo<Context> {
-                context: C>|<
+                context: Cont>|<
             }
         "#;
         assert_completion_excluding_auto_import(
@@ -962,7 +965,7 @@ mod completion_tests {
     #[test]
     async fn test_suggest_function_type_parameters() {
         let src = r#"
-            fn foo<Context>(x: C>|<) {}
+            fn foo<Context>(x: Cont>|<) {}
         "#;
         assert_completion_excluding_auto_import(
             src,
@@ -1557,6 +1560,19 @@ mod completion_tests {
         );
     }
 
+    #[test]
+    async fn test_completes_matching_any_part_of_an_identifier_by_underscore() {
+        let src = r#"
+            struct Foo {
+                some_property: i32,
+            }
+
+            fn foo(f: Foo) {
+                f.prop>|<
+            }
+        "#;
+        assert_completion(src, vec![field_completion_item("some_property", "i32")]).await;
+
     #[test]
     async fn test_auto_import_with_super() {
         let src = r#"