diff --git a/packages/core/src/openbim/IDSSpecifications/src/Specification.ts b/packages/core/src/openbim/IDSSpecifications/src/Specification.ts
index d3b692d4..36646367 100644
--- a/packages/core/src/openbim/IDSSpecifications/src/Specification.ts
+++ b/packages/core/src/openbim/IDSSpecifications/src/Specification.ts
@@ -1,7 +1,7 @@
 import * as FRAGS from "@thatopen/fragments";
 import { Components } from "../../../core/Components";
 import { IDSCheckResult, IDSSpecificationData, IfcVersion } from "./types";
-import { UUID } from "../../../utils";
+import { UUID, ModelIdMapUtils } from "../../../utils";
 import { IDSFacet } from "./facets";
 import { IDSSpecifications } from "..";
 import { ModelIdMap } from "../../../fragments";
@@ -60,14 +60,19 @@ export class IDSSpecification implements IDSSpecificationData {
 
     if (this.requirements.size === 0) return result;
 
-    // Get applicable elements
-    const entities: ModelIdMap = {};
+    // Get applicable elements. In IDS an element is applicable only when it
+    // matches every applicability facet, so each facet collects its own
+    // matches and the results are intersected.
+    const facetEntities: ModelIdMap[] = [];
     const applicabilityPromises = [];
     for (const facet of this.applicability) {
-      applicabilityPromises.push(facet.getEntities(modelIds, entities));
+      const facetMatches: ModelIdMap = {};
+      facetEntities.push(facetMatches);
+      applicabilityPromises.push(facet.getEntities(modelIds, facetMatches));
     }
 
     await Promise.all(applicabilityPromises);
+    const entities = ModelIdMapUtils.intersect(facetEntities);
 
     // Test applicable elements against requirements
     const requirementPromises = [];
diff --git a/packages/core/src/openbim/IDSSpecifications/src/specification.test.ts b/packages/core/src/openbim/IDSSpecifications/src/specification.test.ts
new file mode 100644
index 00000000..66e19b9b
--- /dev/null
+++ b/packages/core/src/openbim/IDSSpecifications/src/specification.test.ts
@@ -0,0 +1,89 @@
+import * as FRAGS from "@thatopen/fragments";
+import * as fs from "fs";
+import * as path from "path";
+import { afterAll, beforeAll, describe, expect, it, vi } from "vitest";
+import type { Components } from "../../../index";
+import { loadSourceBundle } from "../../../../tests/source-bundle";
+
+// Needs the real `Components`: see `loadSourceBundle`.
+const OBC = await loadSourceBundle();
+
+const MODEL_ID = "type-psets";
+
+// `tests/fixtures/type-psets.ifc` (see facets/property.test.ts): six walls,
+// four of which have Pset_WallCommon.IsExternal = TRUE, directly or through
+// their type.
+const WALLS = [40, 41, 42, 43, 45, 46];
+const WITH_IS_EXTERNAL_TRUE = [40, 41, 42, 46];
+
+const convert = async () => {
+  const importer = new FRAGS.IfcImporter();
+  const root = path.resolve(__dirname, "../../../..");
+  importer.wasm = {
+    path: `${path.resolve(root, "../../node_modules/web-ifc")}/`,
+    absolute: true,
+  };
+  const ifc = fs.readFileSync(
+    path.join(root, "tests", "fixtures", "type-psets.ifc"),
+  );
+  const bytes = await importer.process({
+    bytes: new Uint8Array(ifc),
+    raw: true,
+  });
+  return new FRAGS.SingleThreadedFragmentsModel(MODEL_ID, bytes, true);
+};
+
+describe("IDSSpecification applicability", () => {
+  let components: Components;
+  let model: FRAGS.SingleThreadedFragmentsModel;
+
+  beforeAll(async () => {
+    model = await convert();
+    components = new OBC.Components();
+    const fragments = components.get(OBC.FragmentsManager);
+    vi.spyOn(fragments, "list", "get").mockReturnValue(
+      new Map([[MODEL_ID, model]]) as never,
+    );
+  }, 60_000);
+
+  afterAll(() => {
+    vi.restoreAllMocks();
+    components?.dispose();
+    model?.dispose();
+  });
+
+  const wall = () =>
+    new OBC.IDSEntity(components, { type: "simple", parameter: "IFCWALL" });
+
+  const isExternal = () => {
+    const property = new OBC.IDSProperty(
+      components,
+      { type: "simple", parameter: "Pset_WallCommon" },
+      { type: "simple", parameter: "IsExternal" },
+    );
+    property.value = { type: "simple", parameter: true };
+    return property;
+  };
+
+  const tested = async (
+    ...applicability: InstanceType<typeof OBC.IDSFacet>[]
+  ) => {
+    const spec = components
+      .get(OBC.IDSSpecifications)
+      .create("applicability", ["IFC4"]);
+    for (const facet of applicability) spec.applicability.add(facet);
+    spec.requirements.add(wall());
+    const result = await spec.test([new RegExp(MODEL_ID)]);
+    return [...(result.get(MODEL_ID)?.keys() ?? [])].sort((a, b) => a - b);
+  };
+
+  it("tests every element a single facet selects", async () => {
+    expect(await tested(wall())).toEqual(WALLS);
+  });
+
+  it("tests only the elements that match every applicability facet", async () => {
+    // IDS: applicability facets are combined with AND, so "a wall that is
+    // external" must not test the two walls that are not.
+    expect(await tested(wall(), isExternal())).toEqual(WITH_IS_EXTERNAL_TRUE);
+  });
+});