diff --git a/crates/ra_hir_def/src/nameres/collector.rs b/crates/ra_hir_def/src/nameres/collector.rs
index 7e60839614f0..6db9937a4321 100644
--- a/crates/ra_hir_def/src/nameres/collector.rs
+++ b/crates/ra_hir_def/src/nameres/collector.rs
@@ -36,11 +36,12 @@ pub(super) fn collect_defs(db: &impl DefDatabase2, mut def_map: CrateDefMap) ->
         );
 
         // look for the prelude
-        if def_map.prelude.is_none() {
-            let map = db.crate_def_map(dep.crate_id);
-            if map.prelude.is_some() {
-                def_map.prelude = map.prelude;
-            }
+        // If the dependency defines a prelude, we overwrite an already defined
+        // prelude. This is necessary to import the "std" prelude if a crate
+        // depends on both "core" and "std".
+        let dep_def_map = db.crate_def_map(dep.crate_id);
+        if dep_def_map.prelude.is_some() {
+            def_map.prelude = dep_def_map.prelude;
         }
     }
 
diff --git a/crates/ra_hir_def/src/nameres/tests.rs b/crates/ra_hir_def/src/nameres/tests.rs
index 52bd0aa91e8c..256f7d4be72e 100644
--- a/crates/ra_hir_def/src/nameres/tests.rs
+++ b/crates/ra_hir_def/src/nameres/tests.rs
@@ -463,6 +463,37 @@ fn values_dont_shadow_extern_crates() {
     "###);
 }
 
+#[test]
+fn std_prelude_takes_precedence_above_core_prelude() {
+    let map = def_map(
+        r#"
+        //- /main.rs crate:main deps:core,std
+        use {Foo, Bar};
+
+        //- /std.rs crate:std deps:core
+        #[prelude_import]
+        pub use self::prelude::*;
+        mod prelude {
+            pub struct Foo;
+            pub use core::prelude::Bar;
+        }
+
+        //- /core.rs crate:core
+        #[prelude_import]
+        pub use self::prelude::*;
+        mod prelude {
+            pub struct Bar;
+        }
+        "#,
+    );
+
+    assert_snapshot!(map, @r###"
+        ⋮crate
+        ⋮Bar: t v
+        ⋮Foo: t v
+    "###);
+}
+
 #[test]
 fn cfg_not_test() {
     let map = def_map(
diff --git a/crates/ra_ide_api/src/completion/complete_scope.rs b/crates/ra_ide_api/src/completion/complete_scope.rs
index 4e56de3f5424..3e205efd12ae 100644
--- a/crates/ra_ide_api/src/completion/complete_scope.rs
+++ b/crates/ra_ide_api/src/completion/complete_scope.rs
@@ -597,6 +597,68 @@ mod tests {
         );
     }
 
+    #[test]
+    fn completes_std_prelude_if_core_is_defined() {
+        assert_debug_snapshot!(
+            do_reference_completion(
+                "
+                //- /main.rs
+                fn foo() { let x: <|> }
+
+                //- /core/lib.rs
+                #[prelude_import]
+                use prelude::*;
+
+                mod prelude {
+                    struct Option;
+                }
+
+                //- /std/lib.rs
+                #[prelude_import]
+                use prelude::*;
+
+                mod prelude {
+                    struct String;
+                }
+                "
+            ),
+            @r###"
+        [
+            CompletionItem {
+                label: "String",
+                source_range: [18; 18),
+                delete: [18; 18),
+                insert: "String",
+                kind: Struct,
+            },
+            CompletionItem {
+                label: "core",
+                source_range: [18; 18),
+                delete: [18; 18),
+                insert: "core",
+                kind: Module,
+            },
+            CompletionItem {
+                label: "foo()",
+                source_range: [18; 18),
+                delete: [18; 18),
+                insert: "foo()$0",
+                kind: Function,
+                lookup: "foo",
+                detail: "fn foo()",
+            },
+            CompletionItem {
+                label: "std",
+                source_range: [18; 18),
+                delete: [18; 18),
+                insert: "std",
+                kind: Module,
+            },
+        ]
+        "###
+        );
+    }
+
     #[test]
     fn completes_macros_as_value() {
         assert_debug_snapshot!(
diff --git a/crates/ra_project_model/src/lib.rs b/crates/ra_project_model/src/lib.rs
index 8b8663a78fcf..0e14f1b70c9f 100644
--- a/crates/ra_project_model/src/lib.rs
+++ b/crates/ra_project_model/src/lib.rs
@@ -199,6 +199,7 @@ impl ProjectWorkspace {
                     }
                 }
 
+                let libcore = sysroot.core().and_then(|it| sysroot_crates.get(&it).copied());
                 let libstd = sysroot.std().and_then(|it| sysroot_crates.get(&it).copied());
 
                 let mut pkg_to_lib_crate = FxHashMap::default();
@@ -226,7 +227,7 @@ impl ProjectWorkspace {
                         }
                     }
 
-                    // Set deps to the std and to the lib target of the current package
+                    // Set deps to the core, std and to the lib target of the current package
                     for &from in pkg_crates.get(&pkg).into_iter().flatten() {
                         if let Some(to) = lib_tgt {
                             if to != from {
@@ -240,6 +241,13 @@ impl ProjectWorkspace {
                                 }
                             }
                         }
+                        // core is added as a dependency before std in order to
+                        // mimic rustcs dependency order
+                        if let Some(core) = libcore {
+                            if let Err(_) = crate_graph.add_dep(from, "core".into(), core) {
+                                log::error!("cyclic dependency on core for {}", pkg.name(&cargo))
+                            }
+                        }
                         if let Some(std) = libstd {
                             if let Err(_) = crate_graph.add_dep(from, "std".into(), std) {
                                 log::error!("cyclic dependency on std for {}", pkg.name(&cargo))
diff --git a/crates/ra_project_model/src/sysroot.rs b/crates/ra_project_model/src/sysroot.rs
index 35d6df5cb5d7..3d827809ee80 100644
--- a/crates/ra_project_model/src/sysroot.rs
+++ b/crates/ra_project_model/src/sysroot.rs
@@ -27,6 +27,10 @@ struct SysrootCrateData {
 }
 
 impl Sysroot {
+    pub fn core(&self) -> Option<SysrootCrate> {
+        self.by_name("core")
+    }
+
     pub fn std(&self) -> Option<SysrootCrate> {
         self.by_name("std")
     }