diff --git a/packages/cubejs-schema-compiler/src/adapter/BaseTimeDimension.ts b/packages/cubejs-schema-compiler/src/adapter/BaseTimeDimension.ts
index 7f8869bc4968a..69c7a4ffa2ace 100644
--- a/packages/cubejs-schema-compiler/src/adapter/BaseTimeDimension.ts
+++ b/packages/cubejs-schema-compiler/src/adapter/BaseTimeDimension.ts
@@ -273,7 +273,7 @@ export class BaseTimeDimension extends BaseFilter {
   }
 
   public resolvedGranularity() {
-    return this.granularityObj ? this.granularityObj.resolvedGranularity() : this.dateRangeGranularity();
+    return this.granularityObj ? this.granularityObj.resolvedGranularity() : null;
   }
 
   public wildcardRange() {
diff --git a/packages/cubejs-schema-compiler/src/adapter/PreAggregations.js b/packages/cubejs-schema-compiler/src/adapter/PreAggregations.js
index cd2b1c2015f22..c23cfd418fb0b 100644
--- a/packages/cubejs-schema-compiler/src/adapter/PreAggregations.js
+++ b/packages/cubejs-schema-compiler/src/adapter/PreAggregations.js
@@ -604,6 +604,9 @@ export class PreAggregations {
      */
     const expandTimeDimension = (timeDimension) => {
       const [dimension, resolvedGranularity] = timeDimension;
+      if (!resolvedGranularity) {
+        return [[dimension, '*']]; // Any granularity should fit
+      }
       return expandGranularity(dimension, resolvedGranularity)
         .map((newGranularity) => [dimension, newGranularity]);
     };
@@ -638,7 +641,13 @@ export class PreAggregations {
 
       const timeDimensionsMatch = (timeDimensionsList, doBackAlias) => R.allPass(
         timeDimensionsList.map(
-          tds => R.anyPass(tds.map(td => R.contains(td)))
+          tds => R.anyPass(tds.map(td => {
+            if (td[1] === '*') {
+              return R.any(tdtc => tdtc[0] === td[0]); // need to match the dimension at least
+            } else {
+              return R.contains(td);
+            }
+          }))
         )
       )(
         doBackAlias ?
diff --git a/packages/cubejs-schema-compiler/test/integration/postgres/pre-agg-allow-non-strict.test.ts b/packages/cubejs-schema-compiler/test/integration/postgres/pre-agg-allow-non-strict.test.ts
index dee82a3d3b875..0a19233ab49cc 100644
--- a/packages/cubejs-schema-compiler/test/integration/postgres/pre-agg-allow-non-strict.test.ts
+++ b/packages/cubejs-schema-compiler/test/integration/postgres/pre-agg-allow-non-strict.test.ts
@@ -195,6 +195,16 @@ const getQueries = (compiler, joinGraph, cubeEvaluator) => ([
     }],
     timezone: 'America/Los_Angeles',
   }),
+  // no granularity
+  new PostgresQuery({ joinGraph, cubeEvaluator, compiler }, {
+    measures: ['cube.totalQuantity', 'cube.totalProfit'],
+    dimensions: ['cube.city'],
+    timeDimensions: [{
+      dimension: 'cube.orderDate',
+      dateRange: ['2020-01-01 00:00:00.000', '2020-03-30 22:50:50.999'],
+    }],
+    timezone: 'America/Los_Angeles',
+  }),
 ]);
 
 describe(
@@ -259,6 +269,15 @@ describe(
         expect(query.indexOf('cube__daily_data')).toEqual(-1);
         expect(query.indexOf('cube__hourly_data')).toEqual(-1);
       });
+
+      it('query with no granularity match MonthlyData', async () => {
+        await compiler.compile();
+        const [,,,,,, request] = getQueries(compiler, joinGraph, cubeEvaluator);
+        const [query] = request.buildSqlAndParams();
+        expect(query.indexOf('cube__monthly_data')).toBeGreaterThanOrEqual(0);
+        expect(query.indexOf('cube__daily_data')).toEqual(-1);
+        expect(query.indexOf('cube__hourly_data')).toEqual(-1);
+      });
     });
 
     describe('The `DailyData` pre-aggregation with the `allowNonStrictDateRangeMatch` enabled', () => {
@@ -320,6 +339,15 @@ describe(
         expect(query.indexOf('cube__daily_data')).toBeGreaterThanOrEqual(0);
         expect(query.indexOf('cube__hourly_data')).toEqual(-1);
       });
+
+      it('query with no granularity match MonthlyData', async () => {
+        await compiler.compile();
+        const [,,,,,, request] = getQueries(compiler, joinGraph, cubeEvaluator);
+        const [query] = request.buildSqlAndParams();
+        expect(query.indexOf('cube__monthly_data')).toEqual(-1);
+        expect(query.indexOf('cube__daily_data')).toBeGreaterThanOrEqual(0);
+        expect(query.indexOf('cube__hourly_data')).toEqual(-1);
+      });
     });
 
     describe('The `HourlyData` pre-aggregation with the `allowNonStrictDateRangeMatch` enabled', () => {
@@ -381,6 +409,15 @@ describe(
         expect(query.indexOf('cube__daily_data')).toEqual(-1);
         expect(query.indexOf('cube__hourly_data')).toBeGreaterThanOrEqual(0);
       });
+
+      it('query with no granularity match HourlyData', async () => {
+        await compiler.compile();
+        const [,,,,,, request] = getQueries(compiler, joinGraph, cubeEvaluator);
+        const [query] = request.buildSqlAndParams();
+        expect(query.indexOf('cube__monthly_data')).toEqual(-1);
+        expect(query.indexOf('cube__daily_data')).toEqual(-1);
+        expect(query.indexOf('cube__hourly_data')).toBeGreaterThanOrEqual(0);
+      });
     });
 
     describe('`MonthlyData` and `DailyData` pre-aggregations with the `allowNonStrictDateRangeMatch` enabled', () => {