diff --git a/firedrake/assemble.py b/firedrake/assemble.py
index 181909161e..82d4ca80db 100644
--- a/firedrake/assemble.py
+++ b/firedrake/assemble.py
@@ -1610,7 +1610,7 @@ def _integral_type(self):
 
     @cached_property
     def _mesh(self):
-        return self._form.ufl_domains()[self._kinfo.domain_number]
+        return tuple(self._form.ufl_domains())[self._kinfo.domain_number]
 
     @cached_property
     def _needs_subset(self):
@@ -1731,7 +1731,7 @@ def _as_global_kernel_arg_coefficient(_, self):
 
     ufl_element = V.ufl_element()
     if ufl_element.family() == "Real":
-        return op2.GlobalKernelArg((ufl_element.value_size,))
+        return op2.GlobalKernelArg((V.value_size,))
     else:
         return self._make_dat_global_kernel_arg(V, index=index)
 
@@ -1945,7 +1945,7 @@ def _indexed_tensor(self):
 
     @cached_property
     def _mesh(self):
-        return self._form.ufl_domains()[self._kinfo.domain_number]
+        return tuple(self._form.ufl_domains())[self._kinfo.domain_number]
 
     @cached_property
     def _iterset(self):
diff --git a/firedrake/slate/slac/compiler.py b/firedrake/slate/slac/compiler.py
index 1333a04039..7e1b14281c 100644
--- a/firedrake/slate/slac/compiler.py
+++ b/firedrake/slate/slac/compiler.py
@@ -82,7 +82,8 @@ def _compile_expression_hashkey(slate_expr, compiler_parameters=None):
 
 def _compile_expression_comm(*args, **kwargs):
     # args[0] is a slate_expr
-    return args[0].ufl_domains()[0].comm
+    domain, = args[0].ufl_domains()
+    return domain.comm
 
 
 @memory_and_disk_cache(
diff --git a/firedrake/slate/slate.py b/firedrake/slate/slate.py
index 79b65ba79a..8176b9d57d 100644
--- a/firedrake/slate/slate.py
+++ b/firedrake/slate/slate.py
@@ -247,11 +247,11 @@ def ufl_domain(self):
 
         The function will fail if multiple domains are found.
         """
-        domains = self.ufl_domains()
-        assert all(domain == domains[0] for domain in domains), (
-            "All integrals must share the same domain of integration."
-        )
-        return domains[0]
+        try:
+            domain, = self.ufl_domains()
+        except ValueError:
+            raise ValueError("All integrals must share the same domain of integration.")
+        return domain
 
     @abstractmethod
     def ufl_domains(self):