diff --git a/modules/gapi/src/executor/gstreamingexecutor.cpp b/modules/gapi/src/executor/gstreamingexecutor.cpp
index 41cb83f710..653d20e712 100644
--- a/modules/gapi/src/executor/gstreamingexecutor.cpp
+++ b/modules/gapi/src/executor/gstreamingexecutor.cpp
@@ -13,6 +13,10 @@
 
 #include <opencv2/gapi/opencv_includes.hpp>
 
+#if !defined(GAPI_STANDALONE)
+#include <opencv2/gapi/core.hpp> // GCopy -- FIXME - to be removed!
+#endif // GAPI_STANDALONE
+
 #include "api/gproto_priv.hpp" // ptr(GRunArgP)
 #include "compiler/passes/passes.hpp"
 #include "backends/common/gbackend.hpp" // createMat
@@ -80,6 +84,10 @@ struct DataQueue {
     std::shared_ptr<cv::gimpl::stream::Q> q;
 };
 
+struct DesyncSpecialCase {
+    static const char *name() { return "DesyncSpecialCase"; }
+};
+
 std::vector<cv::gimpl::stream::Q*> reader_queues(      ade::Graph &g,
                                                  const ade::NodeHandle &obj)
 {
@@ -936,19 +944,53 @@ cv::gimpl::GStreamingExecutor::GStreamingExecutor(std::unique_ptr<ade::Graph> &&
                                          , isl_exec
                                          });
                 // Initialize queues for every operation's input
-                ade::TypedGraph<DataQueue> qgr(*m_island_graph);
+                ade::TypedGraph<DataQueue, DesyncSpecialCase> qgr(*m_island_graph);
+                bool is_desync_start = false;
                 for (auto eh : nh->inEdges())
                 {
                     // ...only if the data is not compile-const
                     if (const_ins.count(eh->srcNode()) == 0) {
                         if (m_gim.metadata(eh).contains<DesyncIslEdge>()) {
                             qgr.metadata(eh).set(DataQueue(DataQueue::DESYNC));
+                            is_desync_start = true;
+                        } else if (qgr.metadata(eh).contains<DesyncSpecialCase>()) {
+                            // See comment below
+                            // Limit queue size to 1 in this case
+                            qgr.metadata(eh).set(DataQueue(1u));
                         } else {
                             qgr.metadata(eh).set(DataQueue(queue_capacity));
                         }
                         m_internal_queues.insert(qgr.metadata(eh).get<DataQueue>().q.get());
                     }
                 }
+                // WORKAROUND:
+                // Since now we always know desync() is followed by copy(),
+                // copy is always the island with DesyncIslEdge.
+                // Mark the node's outputs a special way so then its following
+                // queue sizes will be limited to 1 (to avoid copy reading more
+                // data in advance - as there's no other way for the underlying
+                // "slow" part to control it)
+                if (is_desync_start) {
+                    auto isl = m_gim.metadata(nh).get<FusedIsland>().object;
+                    // In the current implementation, such islands
+                    // _must_ start with copy
+                    GAPI_Assert(isl->in_ops().size() == 1u);
+#if !defined(GAPI_STANDALONE)
+                    GAPI_Assert(GModel::Graph(*m_orig_graph)
+                                .metadata(*isl->in_ops().begin())
+                                .get<cv::gimpl::Op>()
+                                .k.name == cv::gapi::core::GCopy::id());
+#endif // GAPI_STANDALONE
+                    for (auto out_nh : nh->outNodes()) {
+                        for (auto out_eh : out_nh->outEdges()) {
+                            qgr.metadata(out_eh).set(DesyncSpecialCase{});
+                        }
+                    }
+                }
+                // It is ok to do it here since the graph is visited in
+                // a topologic order and its consumers (those checking
+                // their input edges & initializing queues) are yet to be
+                // visited
             }
             break;
         case NodeKind::SLOT: