diff --git a/compiler/src/app.rs b/compiler/src/app.rs
index ca1f7cd..f014d01 100644
--- a/compiler/src/app.rs
+++ b/compiler/src/app.rs
@@ -23,7 +23,7 @@ pub fn target(name: &str) -> Target {
     }
 }
 
-/// `{entry, css, modules: {path: {code, map}}}`, or `{diagnostics: [...]}` / `{error}`. `entry` is an absolute path.
+/// `{entry, css, modules: {path: {code, map, css}}}` (the program's stylesheet, and each module's own), or `{diagnostics: [...]}` / `{error}`. `entry` is an absolute path.
 /// `spa`: a client-only build, checked under 08 CN-3d.
 pub fn app(entry: &str, target: Target, module_name: &str, spa: bool) -> Value {
     // module keys are POSIX paths (`modules::join_path`); Windows takes `D:/a/b.rx` as it takes `D:\a\b.rx`
@@ -49,7 +49,7 @@ pub fn app(entry: &str, target: Target, module_name: &str, spa: bool) -> Value {
             let path = &out.paths[name];
             let text = read_disk(path).unwrap_or_default();
             let l = lower_view(module, path, target, module_name, Some((path, &text))).map_err(|e| json!({ "error": e }))?;
-            modules.insert(path.clone(), json!({ "code": l.code, "map": l.map }));
+            modules.insert(path.clone(), json!({ "code": l.code, "map": l.map, "css": out.module_css[name] }));
         }
         Ok(json!({ "entry": set.entry, "css": out.css, "modules": modules }))
     })()
diff --git a/compiler/src/emit.rs b/compiler/src/emit.rs
index ffc44a3..1338360 100644
--- a/compiler/src/emit.rs
+++ b/compiler/src/emit.rs
@@ -180,6 +180,8 @@ pub struct Compiled {
     pub entry: String,
     /// CSS-4: the modules' stylesheets, beside their JavaScript
     pub css: String,
+    /// CSS-4: each module's own stylesheet, by its output name
+    pub module_css: IndexMap<String, String>,
 }
 
 /// 09 MO-1: one ES module per `.rx` module. A dependency's module is a factory over the app (`__rt.module` runs it once per
@@ -197,8 +199,10 @@ pub fn compile_linked(set: &ModuleSet, extra: &[Vec<Stmt>], by_source: bool) ->
     g.by_source = by_source;
     let mut files = IndexMap::new();
     let mut paths = IndexMap::new();
+    let mut module_css = IndexMap::new();
     for path in &set.order {
         let p = &set.programs[path];
+        let css0 = g.css.len();
         g.begin_module(path, &p.decls);
         let mut deps: Vec<&str> = vec![];
         for d in &p.decls {
@@ -232,10 +236,11 @@ pub fn compile_linked(set: &ModuleSet, extra: &[Vec<Stmt>], by_source: bool) ->
             fbody.append(&mut inner);
             body.push(S::ExportDefault(Func { name: Some("module".into()), params: vec![P::Id("__rt".into())], directives: vec![], body: fbody, is_async: false, generator: false }));
         }
+        module_css.insert(g.out(path), g.css[css0..].join("\n"));
         files.insert(g.out(path), body);
         paths.insert(g.out(path), path.clone());
     }
-    Ok(Compiled { files, paths, entry: g.out(&set.entry), css: g.css.join("\n") })
+    Ok(Compiled { files, paths, entry: g.out(&set.entry), css: g.css.join("\n"), module_css })
 }
 
 struct Gen<'p> {
diff --git a/compiler/test/vite.mjs b/compiler/test/vite.mjs
index 44454d5..05af552 100644
--- a/compiler/test/vite.mjs
+++ b/compiler/test/vite.mjs
@@ -118,9 +118,51 @@ if (!filter || "shared".includes(filter)) {   // two programs on one page, shari
 if (!filter || "todo".includes(filter)) {   // the dev server: modules transformed on request
   const dir = project("todo-dev", "todo.rx");
   const server = await vite.createServer(config(dir, "todo.rx")); await server.listen(0);
-  await drive("todo (dev)", `http://127.0.0.1:${server.httpServer.address().port}/`, todo);
+  await drive("todo (dev)", server.resolvedUrls.local[0], todo);
   await server.close();
 }
+if (!filter || "styles".includes(filter)) {   // CSS-4 under the dev server: a dependency's <style> edit reaches the page
+  const dir = project("styles-dev", "styled/main.rx");
+  mkdirSync(path.join(dir, "src/styled"));
+  writeFileSync(path.join(dir, "src/styled/main.rx"), `import { Badge } from "./badge.rx"\n\nexport default component Main() {\n  <main><Badge /></main>\n}\n`);
+  const badge = path.join(dir, "src/styled/badge.rx");
+  const style = color => `export component Badge() {\n  <style>\n    .badge { color: ${color} }\n  </style>\n  <p class="badge">badge</p>\n}\n`;
+  writeFileSync(badge, style("rgb(0, 0, 255)"));
+  const server = await vite.createServer(config(dir, "styled/main.rx")); await server.listen(0);
+  const url = server.resolvedUrls.local[0];
+  const color = page => page.$eval(".badge", e => getComputedStyle(e).color);
+  const until = async (page, want, what) => {
+    for (let i = 0; i < 40 && await color(page).catch(() => "") !== want; i++) await page.waitForTimeout(100);
+    const got = await color(page).catch(e => e.message.split("\n")[0]); if (got !== want) throw new Error(`${what}: color ${got}, not ${want}`);
+  };
+  await drive("styles (dev)", url, async page => {
+    await until(page, "rgb(0, 0, 255)", "first load");
+    writeFileSync(badge, style("rgb(255, 0, 0)"));
+    await until(page, "rgb(255, 0, 0)", "after the edit");
+    await page.reload(); await until(page, "rgb(255, 0, 0)", "after a reload");
+    const fresh = await browser.newPage();
+    try { await fresh.goto(url); await until(fresh, "rgb(255, 0, 0)", "in a new page"); } finally { await fresh.close(); }
+  });
+  await server.close();
+}
+if (!filter || "cold".includes(filter)) {   // a dependency asked for before its entry, as Vitest's `fsModuleCache` leaves it
+  const { default: rx } = await import(pathToFileURL(path.join(pkg, "vite.mjs")).href);
+  const root = project("cold", "shop/main.rx"), catalog = path.join(root, "src/shop/catalog.rx");
+  const ctx = (id, moduleId) => ({ id, moduleId, root, ssr: false, solid: { generate: "dom", hydratable: false }, addWatchFile() {} });
+  try {
+    // a commented-out import is not an edge: read as one, it would make main.rx look imported and leave no entry
+    writeFileSync(catalog, readFileSync(catalog, "utf8") + `\n// import { x } from "./main.rx"\n`);
+    const warm = rx(); warm.compile("", ctx(path.join(root, "src/shop/main.rx"), path.join(root, "src/shop/main.rx")));
+    const want = warm.compile("", ctx(catalog, `${catalog}?rx-dep`)).code;
+    const got = rx().compile("", ctx(catalog, `${catalog}?rx-dep`)).code;
+    if (got !== want) throw new Error("the dependency compiled cold differs from the one compiled after its entry");
+    writeFileSync(catalog, readFileSync(catalog, "utf8") + "\nexport bad = missingName\n");
+    let report = "";
+    try { rx().compile("", ctx(catalog, `${catalog}?rx-dep`)); } catch (e) { report = e.message; }
+    if (!/catalog\.rx:\d+(:\d+)?: error /.test(report)) throw new Error(`a cold dependency that does not compile reports ${JSON.stringify(report.slice(0, 200))}`);
+    pass++; console.log("✓ cold dependency: compiled from the program that holds it, or that program's diagnostics");
+  } catch (e) { fail++; console.log(`✗ cold dependency: ${e.message.split("\n")[0]}`); }
+}
 await browser.close();
 console.log(`\n${pass} pass, ${fail} fail (vite ${vite.version}, @solidjs/vite-plugin ${JSON.parse(readFileSync(path.join(pluginDir, "package.json"), "utf8")).version})`);
 process.exit(fail ? 1 : 0);
diff --git a/compiler/vite.mjs b/compiler/vite.mjs
index d65161b..ed6f027 100644
--- a/compiler/vite.mjs
+++ b/compiler/vite.mjs
@@ -3,8 +3,8 @@
 // names it explicitly.
 //
 // The crate (its Node-API build, `src/node.rs`: what `rxc app` does) already hands each module to Solid's compiler
-// (spec/11 CP-1), so a `.rx` module comes back as Solid's output for the environment's `generate`, with its source map onto the `.rx` and, on a
-// program's entry, the program's stylesheet. Solid's plugin then takes it the way it takes lowered `.tsrx`: primitive
+// (spec/11 CP-1), so a `.rx` module comes back as Solid's output for the environment's `generate`, with its source map onto the `.rx` and
+// its own stylesheet. Solid's plugin then takes it the way it takes lowered `.tsrx`: primitive
 // names, `lazy()`, the HMR refresh pass, server functions (12 SF-7a), the stylesheet as a CSS module.
 //
 // Entries find themselves. JavaScript imports only a program's entry (its default export mounts the app); an `.rx`
@@ -13,7 +13,7 @@
 // changes. The crate's output imports its dependencies as `./x.rx?rx-dep`, and a dependency is served from the build
 // of a program that contains it. A module several programs share is one module: its instance is keyed by its factory
 // (11 CP-4b `module`), not by its place in a program.
-import { existsSync, statSync } from "node:fs";
+import { existsSync, readdirSync, readFileSync, statSync } from "node:fs";
 import { createRequire } from "node:module";
 import path from "node:path";
 import { fileURLToPath } from "node:url";
@@ -35,6 +35,29 @@ const isDep = moduleId => new URLSearchParams(moduleId.split("?")[1] ?? "").has(
 // `import __m0 from "./catalog.rx";` → `"./catalog.rx?rx-dep"` (one line each: the module's map is by line, CP-1c)
 const tagDeps = code => code.replace(/^(import \w+ from ")(\.{1,2}\/[^"?]*\.rx)(";?)$/gm, `$1$2?${DEP}$3`);
 
+const RX_IMPORT = /^import\b[^"']*?\bfrom\s+(["'])(\.{1,2}\/[^"'?]*\.rx)\1/gm;
+/** The `.rx` files under `root` from which `file` is reached by imports: first those no other `.rx` file imports. */
+function entriesOf(file, root) {
+  const importers = new Map();
+  const walk = dir => {
+    for (const e of readdirSync(dir, { withFileTypes: true })) {
+      if (e.name === "node_modules" || e.name.startsWith(".")) continue;
+      const p = path.join(dir, e.name);
+      if (e.isDirectory()) walk(p);
+      else if (e.name.endsWith(".rx")) for (const [, , spec] of readFileSync(p, "utf8").matchAll(RX_IMPORT)) {
+        const dep = path.resolve(path.dirname(p), spec);
+        importers.set(dep, [...(importers.get(dep) ?? []), p]);
+      }
+    }
+  };
+  walk(root);
+  const seen = new Set([file]);
+  for (const f of seen) for (const i of importers.get(f) ?? []) seen.add(i);
+  seen.delete(file);
+  const top = f => !importers.has(f);
+  return [...seen].sort().sort((a, b) => top(b) - top(a));
+}
+
 /** @returns {import("@solidjs/vite-plugin").Frontend} */
 export default function rx() {
   const builds = new Map();   // entry\0target\0moduleName\0spa → { entry, target, moduleName, spa, out, stamps }
@@ -50,28 +73,38 @@ export default function rx() {
     builds.set(key, b);
     return b;
   }
+  const built = (file, target, moduleName, spa) =>
+    [...builds.values()].filter(b => b.target === target && b.moduleName === moduleName && b.spa === spa && b.out.modules?.[file]);
   /** A dependency: from a build of a program that has it, rebuilt if that program changed. */
-  function containing(file, target, moduleName, spa) {
-    const has = [...builds.values()].filter(b => b.target === target && b.moduleName === moduleName && b.spa === spa && b.out.modules?.[file]);
+  function containing(file, target, moduleName, spa, root) {
+    const has = built(file, target, moduleName, spa);
     const b = has.find(fresh) ?? has[0];
-    if (!b) throw new Error(`${file} is imported as an .rx dependency, but no program built so far contains it`);
-    return build(b.entry, target, moduleName, spa);
+    if (b) return build(b.entry, target, moduleName, spa);
+    // the entry's compile was skipped (Vitest's `fsModuleCache` served it), so find the program from the files
+    let failed;
+    for (const entry of entriesOf(file, root)) {
+      const found = build(entry, target, moduleName, spa);
+      if (found.out.modules?.[file]) return found;
+      if (!failed && found.out.diagnostics) failed = found;   // the program holds it but does not compile: report why
+    }
+    if (failed) return failed;
+    throw new Error(`${file} is imported as an .rx dependency, but no program under ${root} contains it`);
   }
   return {
-    compile(_source, { id, moduleId, solid, addWatchFile }) {
+    compile(_source, { id, moduleId, root, solid, addWatchFile }) {
       const file = path.resolve(id);
       const target = solid.generate === "ssr" ? "ssr" : solid.generate === "universal" ? "universal" : "dom";
       const moduleName = solid.moduleName ?? "@solidjs/web";
       // 08 CN-3d: a client-only build (no SSR, nothing hydrates) has nothing to show on a first load nothing holds
       const spa = target === "dom" && solid.hydratable === false;
       const dep = isDep(moduleId);
-      const { entry, out } = dep ? containing(file, target, moduleName, spa) : build(file, target, moduleName, spa);
+      const { out } = dep ? containing(file, target, moduleName, spa, path.resolve(root ?? process.cwd())) : build(file, target, moduleName, spa);
       if (out.diagnostics) throw new Error(report(out.diagnostics));
       if (out.error) throw new Error(out.error);
       const m = out.modules[file];
       for (const p of Object.keys(out.modules)) if (p !== file) addWatchFile(p);
-      // CSS-4: the program's stylesheet, linked once, from its entry
-      return { code: tagDeps(m.code), map: m.map, css: !dep && file === entry ? out.css : "" };
+      // CSS-4: each module links its own stylesheet, so a module several programs share links it once
+      return { code: tagDeps(m.code), map: m.map, css: m.css ?? "" };
     },
   };
 }