diff --git a/src/core/document.js b/src/core/document.js
index 9069a0cd7..bac2e281b 100644
--- a/src/core/document.js
+++ b/src/core/document.js
@@ -16,7 +16,7 @@
 import {
   assert, FormatError, getInheritableProperty, info, isArrayBuffer, isBool,
   isNum, isSpace, isString, MissingDataException, OPS, shadow, stringToBytes,
-  stringToPDFString, Util, warn
+  stringToPDFString, Util, warn, XRefEntryException, XRefParseException
 } from '../shared/util';
 import { Catalog, ObjectLoader, XRef } from './obj';
 import { Dict, isDict, isName, isStream, Ref } from './primitives';
@@ -649,6 +649,20 @@ var PDFDocument = (function PDFDocumentClosure() {
       });
     },
 
+    checkFirstPage() {
+      return this.getPage(0).catch((reason) => {
+        if (reason instanceof XRefEntryException) {
+          // Clear out the various caches to ensure that we haven't stored any
+          // inconsistent and/or incorrect state, since that could easily break
+          // subsequent `this.getPage` calls.
+          this._pagePromises.length = 0;
+          this.cleanup();
+
+          throw new XRefParseException();
+        }
+      });
+    },
+
     cleanup: function PDFDocument_cleanup() {
       return this.catalog.cleanup();
     },
diff --git a/src/core/obj.js b/src/core/obj.js
index 700a4ca35..c47d90621 100644
--- a/src/core/obj.js
+++ b/src/core/obj.js
@@ -17,7 +17,7 @@ import {
   bytesToString, createPromiseCapability, createValidAbsoluteUrl, FormatError,
   info, InvalidPDFException, isBool, isNum, isString, MissingDataException,
   PermissionFlag, shadow, stringToPDFString, stringToUTF8String,
-  toRomanNumerals, unreachable, warn, XRefParseException
+  toRomanNumerals, unreachable, warn, XRefEntryException, XRefParseException
 } from '../shared/util';
 import {
   Dict, isCmd, isDict, isName, isRef, isRefsEqual, isStream, Ref, RefSet,
@@ -1473,7 +1473,7 @@ var XRef = (function XRefClosure() {
       if (xrefEntry.uncompressed) {
         xrefEntry = this.fetchUncompressed(ref, xrefEntry, suppressEncryption);
       } else {
-        xrefEntry = this.fetchCompressed(xrefEntry, suppressEncryption);
+        xrefEntry = this.fetchCompressed(ref, xrefEntry, suppressEncryption);
       }
       if (isDict(xrefEntry)) {
         xrefEntry.objId = ref.toString();
@@ -1483,12 +1483,11 @@ var XRef = (function XRefClosure() {
       return xrefEntry;
     },
 
-    fetchUncompressed: function XRef_fetchUncompressed(ref, xrefEntry,
-                                                       suppressEncryption) {
+    fetchUncompressed(ref, xrefEntry, suppressEncryption = false) {
       var gen = ref.gen;
       var num = ref.num;
       if (xrefEntry.gen !== gen) {
-        throw new FormatError('inconsistent generation in XRef');
+        throw new XRefEntryException(`Inconsistent generation in XRef: ${ref}`);
       }
       var stream = this.stream.makeSubStream(xrefEntry.offset +
                                              this.stream.start);
@@ -1504,7 +1503,7 @@ var XRef = (function XRefClosure() {
         obj2 = parseInt(obj2, 10);
       }
       if (obj1 !== num || obj2 !== gen || !isCmd(obj3)) {
-        throw new FormatError('bad XRef entry');
+        throw new XRefEntryException(`Bad (uncompressed) XRef entry: ${ref}`);
       }
       if (obj3.cmd !== 'obj') {
         // some bad PDFs use "obj1234" and really mean 1234
@@ -1514,7 +1513,7 @@ var XRef = (function XRefClosure() {
             return num;
           }
         }
-        throw new FormatError('bad XRef entry');
+        throw new XRefEntryException(`Bad (uncompressed) XRef entry: ${ref}`);
       }
       if (this.encrypt && !suppressEncryption) {
         xrefEntry = parser.getObj(this.encrypt.createCipherTransform(num, gen));
@@ -1527,8 +1526,7 @@ var XRef = (function XRefClosure() {
       return xrefEntry;
     },
 
-    fetchCompressed: function XRef_fetchCompressed(xrefEntry,
-                                                   suppressEncryption) {
+    fetchCompressed(ref, xrefEntry, suppressEncryption = false) {
       var tableOffset = xrefEntry.offset;
       var stream = this.fetch(new Ref(tableOffset, 0));
       if (!isStream(stream)) {
@@ -1573,7 +1571,7 @@ var XRef = (function XRefClosure() {
       }
       xrefEntry = entries[xrefEntry.gen];
       if (xrefEntry === undefined) {
-        throw new FormatError('bad XRef entry for compressed object');
+        throw new XRefEntryException(`Bad (compressed) XRef entry: ${ref}`);
       }
       return xrefEntry;
     },
diff --git a/src/core/worker.js b/src/core/worker.js
index 83496d86f..910d2692f 100644
--- a/src/core/worker.js
+++ b/src/core/worker.js
@@ -258,33 +258,22 @@ var WorkerMessageHandler = {
       WorkerTasks.splice(i, 1);
     }
 
-    function loadDocument(recoveryMode) {
-      var loadDocumentCapability = createPromiseCapability();
+    async function loadDocument(recoveryMode) {
+      await pdfManager.ensureDoc('checkHeader');
+      await pdfManager.ensureDoc('parseStartXRef');
+      await pdfManager.ensureDoc('parse', [recoveryMode]);
 
-      var parseSuccess = function parseSuccess() {
-        Promise.all([
-          pdfManager.ensureDoc('numPages'),
-          pdfManager.ensureDoc('fingerprint'),
-        ]).then(function([numPages, fingerprint]) {
-          loadDocumentCapability.resolve({
-            numPages,
-            fingerprint,
-          });
-        }, parseFailure);
-      };
+      if (!recoveryMode) {
+        // Check that at least the first page can be successfully loaded,
+        // since otherwise the XRef table is definitely not valid.
+        await pdfManager.ensureDoc('checkFirstPage');
+      }
 
-      var parseFailure = function parseFailure(e) {
-        loadDocumentCapability.reject(e);
-      };
-
-      pdfManager.ensureDoc('checkHeader', []).then(function() {
-        pdfManager.ensureDoc('parseStartXRef', []).then(function() {
-          pdfManager.ensureDoc('parse', [recoveryMode]).then(
-            parseSuccess, parseFailure);
-        }, parseFailure);
-      }, parseFailure);
-
-      return loadDocumentCapability.promise;
+      const [numPages, fingerprint] = await Promise.all([
+        pdfManager.ensureDoc('numPages'),
+        pdfManager.ensureDoc('fingerprint'),
+      ]);
+      return { numPages, fingerprint, };
     }
 
     function getPdfManager(data, evaluatorOptions) {
diff --git a/src/shared/util.js b/src/shared/util.js
index 48ed88be7..daac2f9c3 100644
--- a/src/shared/util.js
+++ b/src/shared/util.js
@@ -472,6 +472,18 @@ var MissingDataException = (function MissingDataExceptionClosure() {
   return MissingDataException;
 })();
 
+const XRefEntryException = (function XRefEntryExceptionClosure() {
+  function XRefEntryException(msg) {
+    this.message = msg;
+  }
+
+  XRefEntryException.prototype = new Error();
+  XRefEntryException.prototype.name = 'XRefEntryException';
+  XRefEntryException.constructor = XRefEntryException;
+
+  return XRefEntryException;
+})();
+
 var XRefParseException = (function XRefParseExceptionClosure() {
   function XRefParseException(msg) {
     this.message = msg;
@@ -1033,6 +1045,7 @@ export {
   UnknownErrorException,
   Util,
   toRomanNumerals,
+  XRefEntryException,
   XRefParseException,
   FormatError,
   arrayByteLength,
diff --git a/test/pdfs/issue10326.pdf.link b/test/pdfs/issue10326.pdf.link
new file mode 100644
index 000000000..43094fad9
--- /dev/null
+++ b/test/pdfs/issue10326.pdf.link
@@ -0,0 +1 @@
+https://github.com/mozilla/pdf.js/files/2643238/test.1.pdf
diff --git a/test/pdfs/issue7496.pdf.link b/test/pdfs/issue7496.pdf.link
new file mode 100644
index 000000000..3786d9161
--- /dev/null
+++ b/test/pdfs/issue7496.pdf.link
@@ -0,0 +1 @@
+https://github.com/mozilla/pdf.js/files/369694/repro-pdf.pdf
diff --git a/test/test_manifest.json b/test/test_manifest.json
index 31000b690..e6f1253bf 100644
--- a/test/test_manifest.json
+++ b/test/test_manifest.json
@@ -1275,6 +1275,22 @@
        "rounds": 1,
        "type": "eq"
     },
+    {  "id": "issue7496",
+       "file": "pdfs/issue7496.pdf",
+       "md5": "b422981ae781166e75c0fb4c3634ed96",
+       "link": true,
+       "rounds": 1,
+       "lastPage": 1,
+       "type": "load"
+    },
+    {  "id": "issue10326",
+       "file": "pdfs/issue10326.pdf",
+       "md5": "015c13b09ef735ea1204f38992c60487",
+       "link": true,
+       "rounds": 1,
+       "lastPage": 1,
+       "type": "load"
+    },
     {  "id": "issue7544",
        "file": "pdfs/issue7544.pdf",
        "md5": "87e3a9fc7d6a6c1bd5b53af6926ce48e",