diff --git a/src/engine/Describe.cpp b/src/engine/Describe.cpp
index 51902d2340..83c836e688 100644
--- a/src/engine/Describe.cpp
+++ b/src/engine/Describe.cpp
@@ -46,7 +46,10 @@ string Describe::getCacheKeyImpl() const {
   // Add the names of the default graphs (from the FROM clauses) to the cache
   // key, in a deterministic order.
   //
-  // TODO: What about the FROM NAMED clauses?
+  // NOTE: The default and named graphs are also part of the cache key of the
+  // `subtree_`. However, the named graphs only determine the result for
+  // `subtree_` (the resouces to be described), whereas the default graphs
+  // also determine which triples for these resources become part of the result.
   const auto& defaultGraphs = describe_.datasetClauses_.defaultGraphs_;
   if (defaultGraphs.has_value()) {
     std::vector<std::string> graphIdVec;
@@ -169,7 +172,9 @@ IdTable Describe::makeAndExecuteJoinWithFullIndex(
   // Compute the result of the `join` and select the columns `?subject`,
   // `?predicate`, `?object`.
   //
-  // TODO: How can the `result` have more columns than those?
+  // NOTE: Typically, the join result has already those exact columns, in which
+  // case the `selectColumns` operation is a no-op. Note sure when this is not
+  // the case, but better safe than sorry.
   auto result = join->getResult();
   IdTable resultTable = result->idTable().clone();
   ColumnIndex s = join->getVariableColumn(V{"?subject"});
diff --git a/src/parser/sparqlParser/SparqlQleverVisitor.cpp b/src/parser/sparqlParser/SparqlQleverVisitor.cpp
index c6b09c5842..28054466db 100644
--- a/src/parser/sparqlParser/SparqlQleverVisitor.cpp
+++ b/src/parser/sparqlParser/SparqlQleverVisitor.cpp
@@ -284,9 +284,9 @@ ParsedQuery Visitor::visit(Parser::DescribeQueryContext* ctx) {
   auto describeClause = parsedQuery::Describe{};
   auto describedResources = visitVector(ctx->varOrIri());
 
-  std::vector<Variable> describedVariables;
   // Convert the describe resources (variables or IRIs) from the format that the
-  // parser delivers to the one that the `Describe` struct expects.
+  // parser delivers to the one that the `parsedQuery::Describe` struct expects.
+  std::vector<Variable> describedVariables;
   for (GraphTerm& resource : describedResources) {
     if (std::holds_alternative<Variable>(resource)) {
       const auto& variable = std::get<Variable>(resource);
@@ -300,13 +300,13 @@ ParsedQuery Visitor::visit(Parser::DescribeQueryContext* ctx) {
     }
   }
 
-  // Parse the FROM and FROM NAMED clauses and store them in the
-  // `describeClause`.
+  // Parse the FROM and FROM NAMED clauses.
   auto datasetClauses = parsedQuery::DatasetClauses::fromClauses(
       visitVector(ctx->datasetClause()));
   describeClause.datasetClauses_ = datasetClauses;
 
-  // Parse the WHERE clause and handle the special case of `DESCRIBE *`.
+  // Parse the WHERE clause and construct a SELECT query from it. For `DESCRIBE
+  // *`, add each visible variable as a resource to describe.
   visitWhereClause(ctx->whereClause(), parsedQuery_);
   if (describedResources.empty()) {
     const auto& visibleVariables =
@@ -319,10 +319,17 @@ ParsedQuery Visitor::visit(Parser::DescribeQueryContext* ctx) {
   selectClause.setSelected(std::move(describedVariables));
   describeClause.whereClause_ = std::move(parsedQuery_);
 
-  // Set up the actual DESCRIBE query, which is implemented as a CONSTRUCT query
-  // of the form `CONSTRUCT { ?subject ?predicate ?object} { ... }`. Note that
-  // the solution modifiers (in particular ORDER BY) are part of this query, not
-  // of the WHERE clause.
+  // Set up the final `ParsedQuery` object for the DESCRIBE query. The clause is
+  // a CONSTRUCT query of the form `CONSTRUCT { ?subject ?predicate ?object} {
+  // ... }`, with the `parsedQuery::Describe` object from above as the root
+  // graph pattern. The solution modifiers (in particular ORDER BY) are part of
+  // the CONSTRUCT query.
+  //
+  // NOTE: The dataset clauses are stored once in `parsedQuery_.datasetClauses_`
+  // (which pertains to the CONSTRUCT query that computes the result of the
+  // DESCRIBE), and once in `parsedQuery_.describeClause_.datasetClauses_`
+  // (which pertains to the SELECT query that computes the resources to be
+  // described).
   parsedQuery_ = ParsedQuery{};
   parsedQuery_.addSolutionModifiers(visit(ctx->solutionModifier()));
   parsedQuery_._rootGraphPattern._graphPatterns.emplace_back(