diff --git a/spec/tests/app.js b/spec/tests/app.js
index 26df05a..d72935a 100644
--- a/spec/tests/app.js
+++ b/spec/tests/app.js
@@ -68,7 +68,10 @@ await describe('empty application XAR', async () => {
   await it('install app', async () => {
     const response = await db.app.install(xarName)
     assert.strictEqual(response.success, false)
-    assert.strictEqual(response.error.message, `experr:EXPATH00 Missing descriptor from package: ${app.packageCollection}/test-empty-app.xar`)
+    const { message } = response.error
+    // eXist-db 7 reports EXPATH007 and prefixes the description
+    assert.ok(message.startsWith('experr:EXPATH00'), message)
+    assert.ok(message.endsWith(`Missing descriptor from package: ${app.packageCollection}/test-empty-app.xar`), message)
   })
 
   await it('cleanup', async () => {
diff --git a/spec/tests/documents.js b/spec/tests/documents.js
index 1027bbd..b4ede96 100644
--- a/spec/tests/documents.js
+++ b/spec/tests/documents.js
@@ -52,6 +52,12 @@ await describe('valid XML', async function () {
   const remoteFileName = '/test.xml'
   const contents = readFileSync('spec/files/test.xml')
 
+  // eXist-db 7 keeps the XML declaration stored with a document unless the
+  // custom omit-original-xml-declaration is set, omit-xml-declaration alone
+  // does not remove it. Pending https://github.com/eXist-db/exist/pull/6277
+  const storedDeclarationKept = parseInt(version, 10) >= 7 &&
+    'eXist-db 7 keeps the stored XML declaration, see eXist-db/exist#6277'
+
   await it('can be uploaded', async function () {
     try {
       const fh = await db.documents.upload(contents)
@@ -65,7 +71,7 @@ await describe('valid XML', async function () {
     }
   })
 
-  await it('read with empty options uses defaults', async function () {
+  await it('read with empty options uses defaults', { todo: storedDeclarationKept }, async function () {
     try {
       const contentBuffer = await db.documents.read(remoteFileName, {})
       const lines = contents.toString().split('\n')
@@ -83,7 +89,7 @@ await describe('valid XML', async function () {
     }
   })
 
-  await it('read without passing options', async function () {
+  await it('read without passing options', { todo: storedDeclarationKept }, async function () {
     try {
       // calling read with just one argument, effectively passing null for options
       const contentBuffer = await db.documents.read(remoteFileName)
@@ -102,7 +108,7 @@ await describe('valid XML', async function () {
     }
   })
 
-  await it('serialized without XML declaration', async function () {
+  await it('serialized without XML declaration', { todo: storedDeclarationKept }, async function () {
     try {
       const options = { 'omit-xml-declaration': 'yes' }
       const lines = contents.toString().split('\n')
diff --git a/spec/tests/rest.js b/spec/tests/rest.js
index 74a8b6e..dce0aaf 100644
--- a/spec/tests/rest.js
+++ b/spec/tests/rest.js
@@ -273,7 +273,12 @@ return $r
     }
   })
 
-  await it('post honors start and max', async function () {
+  // eXist-db 7.0.0-SNAPSHOT ignores the start and max attributes of a posted query
+  // https://github.com/eXist-db/exist/issues/6560
+  const paginationIgnored = parseInt(await db.server.version(), 10) >= 7 &&
+    'eXist-db 7 ignores start and max, see eXist-db/exist#6560'
+
+  await it('post honors start and max', { todo: paginationIgnored }, async function () {
     try {
       const res = await rc.post(xqueryMainModule, 'db/rest-test', { start: 1, max: 1 })
       assert.strictEqual(res.statusCode, 200, 'server responded with status ' + res.statusCode)
@@ -290,7 +295,7 @@ return $r
     }
   })
 
-  await it('post honors just start', async function () {
+  await it('post honors just start', { todo: paginationIgnored }, async function () {
     try {
       const res = await rc.post(xqueryMainModule, 'db/rest-test', { start: 2 })
       assert.strictEqual(res.statusCode, 200, 'server responded with status ' + res.statusCode)
@@ -306,7 +311,7 @@ return $r
     }
   })
 
-  await it('post honors cache', async function () {
+  await it('post honors cache', { todo: paginationIgnored }, async function () {
     try {
       const res = await rc.post(xqueryMainModule, 'db/rest-test', { cache: 'yes', start: 1, max: 1 })
       assert.strictEqual(res.statusCode, 200, 'server responded with status ' + res.statusCode)